Sorry for necroposting, but I just found something that is pertinent to this topic (for those who care about it).
As Brendor stated, 0x267A6 is the limit of support conversations (-1) a unit can have before he/she can no longer start one. However, 0x267B6 is the limit of support conversations (-1) a unit can have before he/she can no longer RECEIVE one.
For example, if 0x267A6 is set as 07 and 0x267B6 is set to 04, then a unit can start 8 conversations and receive 5 of them (with the max number of supports possible being the bigger number - 8).
Make sure to set both 0x267A6 and 0x267B6 to the same value you want the cap to be -1 for the support conversations to activate properly.