This is probably a good idea, not so much on pet bills but on large omnibus bills, where there is one sponsor but the whole assembly is involved directly in the decision making.
Speaking as someone who's been observing and participating in the assembly for about 2 years now, though, the real problem with the SOAP, it seems to me, is the time limit on legislation. I've seen many bills which are uncompleted rushed through because time ran out, with debate still raging on, which isn't a good idea. It might have been necessary in the past due to there only being 2 slots, but with 3 plus the budget available for use I don't think that would be a problem anymore.
I generally agree with this argument. I think the maximum/minimum should certainly be lengthened, if only by a little. The Assembly needs more deliberation on the bills that actually make it to the queue, rather than blow through proposed legislation three quarters of the way through the session. The SOAP isn't broken, rather, there's always a way to improve it, as we've all learned from experience.