Maximum number of trade agreements ?

[gapper4]

I currently own 11 provinces as the Shimazu (difficulty Hard) and most of them have Military Ports. I have two sea-based trade treaties and one land-based one. When I go into the diplomatic screen and mouse over the trade buttons, the game keeps telling me that my trade routes are maxed. Why is that ? I should have a good 5-6 open sea-trade routes available with all the ports that I own.

[Dragooon]

Are your trade routes maxed or are their trade routes maxed?

[gapper4]

Well, for some clans it's theirs but for others, the game says it's mine.