It's the way multiline phones work on a Partner. You can assign lines to the buttons, assign auto line select to Intercom first, and then the lines, but it will only select the lines that show on the set.
In other words, say you program an extension port to have lines 1 through 8 appear, set ALS to Intercom-1-2-3-4-5-6, and then plug in a 6 button (4-line) phone. The set will get Intercom first, and dialing 9 will get you lines 1-2-3-4 only. If they are all in use, you get a busy signal, even though in programming you've got lines 5-8 assigned as well.
With only 4 buttons to play with, go to pool mode, assign the lines to pool 881 so it only takes up one button, and you've got 3 left to use. If they need to be able to put one call on hold and make another outgoing call, use pool 880 which takes up 2 buttons, giving you 2 blanks to program.
Just stage a system and work with it!