Tier 2 & Tier 3 unit suggestions for Sultanate of Rum. Note that this is merely a suggestion. 
TURKOMAN TRIBAL GHAZI (TIER 2)
Early Ottoman (and other post-Ilkhanate Turkish principalities of Anatolia) armies were entirely composed of these tribal ghazi cavalry.
FIEF-HOLDING (TIMARLI) PROVINCIAL SIPAHIS OF ANATOLIA & RUMELIA (TIER 2 & TIER 3)
Quoted from Wikipedia:
• The sipahi were traditionally recruited among Turkic landowners, and thus, the non-Turkic provinces such as Arabia and Maghreb did not have sipahi. Recruitment of non-Turkic sipahi was banned with a 1635 ferman (decree).
• The term refers to all freeborn Ottoman Turkish mounted troops other than akıncı and tribal horsemen in the Ottoman army. The sipahis formed two distinct types of cavalry: feudal-like, provincial timarlı sipahi (timariots) which consisted most of the Ottoman army, and salaried, regular kapıkulu sipahi (sipahi of the Porte), which constituted the cavalry part of the Ottoman household troops.
• If a battle was to be fought in Europe, Rumeli Sipahis took the honorary right flank under the Rumeli beylerbey, while the Anatolian beylerbey and his Sipahis took the left flank; when a battle was in Asia, positions were switched. This way, the Ottoman classical army's flanks wholly consisted of Timariot cavalry, while the center consisted of Janissary infantry and artillery divisions.
• The equipment and tactics differed between the Anatolian and Balkan Timarli Sipahi. The Anatolian Sipahi were equipped and fought as classic horse archers, shooting while galloping, yet they weren't nomadic cavalry and their status was similar to medium cavalry class. Balkan Timarli Sipahis wore chainmail, rode barded horses and carried lances and javelins.
• Timarli Sipahis of the classical Ottoman period usually comprised the bulk of the army and did the majority of the fighting on the battlefield. While infantry troops at the army's center maintained a static battle line, the cavalry flanks constituted its mobile striking arm. During battle, Timarli Sipahi tactics were used, opening the conflict with skirmishes and localized skirmishes with enemy cavalry. Regiments of Timarli Sipahis made charges against weaker or isolated units and retreated back to the main body of troops whenever confronted with heavy cavalry. During one regiment's retreat, other regiments of sipahis may have charged the chasing enemy's flanks. Such tactics served to draw enemy cavalry away from infantry support, break their cohesion, and isolate and overwhelm them with numerical superiority. Anatolian Sipahis had the ability to harass and provoke opposing troops with arrow shots. More heavily equipped Balkan Sipahis carried javelins for protection against enemy horsemen during their tactical retreats. All cavalry flanks of the Ottoman army fought a fluid, mounted type of warfare around the center of the army, which served as a stable pivot.
• The standard equipment of Rumeli Sipahis of the classical Ottoman period consisted of a round shield, lance, kilij, javelins and plated chainmail. Their horses were barded. Standard equipment of Anatolian Sipahis in the same era was a round shield, composite Turkish bow, arrows, kilij (Turkish sword) and leather or felt armor. Besides these, Sipahis of both provinces were equipped with bozdogan and şeşper maces, and aydogan, teber and sagir axes. Anatolian Sipahis sometimes also carried lances.
• Whereas the Sipahis (both Tımarlı and Kapıkulu) were almost exclusively chosen amongst ethnic Turkic landowners, they made great strides of efforts to gain respect within the Ottoman Empire and their political reputation depended on the mistakes of the Janissary. That minor quarrels erupted between the two units is made evident with a Turkmen adage, still used today within Turkey, "Atlı er başkaldırmaz", which, referring to the unruly Janissaries, translates into "Horsemen don't mutiny".
So, Sipahis of Anatolia were medium horse archers whereas Sipahis of Rumelia were heavier equipped lancers. I think there can be two units based on Provincial (Tımarlı) Sipahis:
Sipahi Lancers: Shock cavalry/lancers, based on Sipahis of Rumelia
Sipahi Horse Archers: Medium horse archers, based on Sipahis of Anatolia
I think we should be able to upgrade tier2-sipahis to tier 3. Their helmets can be replaced with chicak helmets at tier 3.
QAPUKULU CAVALRY (SIPAHI OF THE PORTE - TIER 2 & TIER 3)
Quoted from Wikipedia:
• Qapukulu Sipahis (Sipahis of the Porte) were household cavalry troops of the Ottoman Palace. They were the cavalry equivalent of the Janissary household infantry force.
• Silahtars ("weapon masters") were chosen from the best warriors in the Ottoman Empire. Any Ottoman soldier who committed a significant deed on the battlefield could be promoted to the Silahtar division, although normally members of other mounted units, like Timarli Sipahis or one of the other less prestigious of the four divisions of Kapikulu Sipahis, were promoted this way.
• Equipment of Silahtar, Sipahi and Ulufeci divisions was plated mail, chainmail, round shield, sword, composite bow, arrows, lance, bozdogan mace and axe. Their equipment was similar to Rumeli (Balkan) provincial Timarli Sipahis, though they wore brilliant fabrics, prominent hats and bore ornamented polearms.
• In the classical period Ottoman battle formation, Kapikulu Sipahis were positioned back of the army as rearguards. They acted as reserve cavalry and bodyguards of Ottoman sultan and vezirs. Their job included to join and reinforce Ottoman army's flanks which otherwise consisted entirely provincial timariot sipahis.
• The Sipahis of the Porte (Qapukulu Sipahis) were originally founded during the reign of Murad I. Although the Sipahis of the Porte were originally recruited, like the Janissaries, using the devşirme system,[3] by the time of Sultan Mehmed II, they were chosen from the Turkic land-owners within the Empire.
Again there can be 2 units based on Qapukulu:
Qapukulu Sipahis: Very heavy shock cavalry
Silahtar Bodyguard: tier 2/tier 3 bodyguards
I think we should be able to upgrade tier2-qapukulu and silahtar bodyguard to tier 3. Their helmets and plated mail can be replaced with chicak helmets and Ottoman krug armor at tier 3.
AKINJI (TIER 2 & TIER 3)
Literally "raiders".
Quoted from Wikipedia
• In battle their main role was to act as advance troops on the front lines and demoralise the marching opposing army by using guerrilla tactics, and to put them in a state of confusion and shock.[1] They could be likened to a scythe in a wheat field. They would basically hit the enemy with arrows. When attacked in melee, they would retreat while still shooting backwards. They could easily outrun heavy cavalry because they were lightly armed and their horses were bred for speed as opposed to strength. Akinji forces carried swords, lances, shields and battle axes as well, so that in a field of combat, they could face the enemy first and fight melee. In some Ottoman campaigns, such as the Battle of Krbava field, Akinji forces were the only units utilized without any need for Ottoman heavy cavalry or infantry.
• Akinji forces were led by certain families. Well-known akinji families were Malkoįoğlu, Turhanlı, Ömerli, Evrenosoğlu, and Mihalli. These akinji clans were mainly composed of Turkmen tribal warriors with a leading dynasty which descended from the warrior ghazis of the first Ottoman ruler Osman I. Adventurers, soldiers of fortune, mercenaries, warrior dervishes, and civilians looking for fortune and adventure would also join the ranks of akinji gangs.
Akınjıs are basically a light horse archer unit.
Akinjis from Suleimanname
JANISSARIES (TIER 2 & TIER 3)
Household infantry. The illustrations give a general idea of their dress; in contemporary Persian-style paintings they are shown in varied colours including black, blue, red and purple, but 16th Century Europeans were struck by the uniformity of their dress - 'The Make and Colour of their clothes were almost the same, so that you would judge them all to be Servants of one Man'- and the uniform issued appears to have been of coarse blue cloth, though some of the Segmens, like the 33rd Orta, the Avcus (huntsmen), may possibly have worn green. Over a short plain tunic, sometimes worn on its own, they had a short sleeved caftan of near ankle length; its front corners were normally hitched up and tucked into the striped sash, which ended in a gold or silver fringe; beneath were blue trousers and yellow stockings. The characteristic sleeve-cap or 'zarcola' was of white felt with the band and frontal of silver or gilt; senior soldiers or members of picked 'forlorn-hope' groups such as 'Serden-gecti' (head-riskers) or 'Dal kilic' (bare swords) were distinguished by semi-precious stones in the nasal and long heron or bird-of-paradise plume. Apart from the powder horn shown a pouch usually hung from the sash. Except for officers the uniform was notably plain, neither slashed nor decorated.
Note that janissary clothing changed little between 15th and 18th centuries. Robe - tunic + Ak Börk (white hat) was their main appearance for centuries. There can be 4 units based on Janissary corps
Janissary Archers (Tier 2)
Solak Guard Archers (Tier 2)
Janissary Gunners (Tier 3)
Janissary Zırhlı Nefer (Heavy Infantry - Tier 2)
OTHER INFANTRY
Heavy Assault Infantry (Tier 2)
Troops fit for siege battles, they wear the heaviest Ottoman armor of the age (plated mail) and carry iron shields.
Azaps (tier 2)
'Azabs' (bachelors) seem to have been more like the irregular cavalry, volunteers serving for loot, and to have been employed during most of the period. Such troops would be irregulars in basically civilian dress, and their chief weapon was the composite bow, though spears, javelins, swords and shields were also used, and toward the end of the 16th Century irregulars would appear to have carried firearms. Azaps can be a light archer unit and replace tier-1 Rumi archers?
Heavy Archers (tier 2)
This unit can replace tier-1 Turkish archers. Basically armored archers.
ARMY COMPOSITION (field battles)
Early Ottoman armies were almost totally composed of cavalry (tribal Turkoman ghazi), and Ottoman Classical Army had more cavalry than infantry, the following (modern) estimate for the Turkish army at Mohacs (1529) gives a fairly typical make-up:
Infantry - 2,000 Janissaries, 5,000 local levies
Cavalry - 7,000 Sipahis of the Porte (Qapukulu), 10,000 Tımarlı Sipahis from Asia Minor, 15,000 Tımarlı Sipahis from Rumelia, and up to 20,000 Akinjis.
Ottoman Classical Army's battle formation

Turkish Kilij (saber) - there were many types of Kilij, the shorter and more curved ones were known as "pala" for instance.
Pala