It would really kind of suck if all the classic summons were limited to a handful of free companies that are large enough to get a lock on them. The issue I see with this system is you will see a few companies that basically pass the primals around between them, and the smaller ones never get to call them.

For summons I would like to see:
Shiva
Ixion
Phoenix
Cait Sith
The Magus Sisters
Yojimbo

For primals:
Bahamut
Anima