Load up the plane with 5 friends and make up some kind of scenic tour with a lunch destination or something and have them each pay 1/6th of the cost. Talk it up with all your friends and family, this is a pretty good scam to build some cheap multi time but may not be a possability if you're someplace like North Dakota.
This kind of thinking is bordering on violation of the "paying less than the pro rata share of the expenses for the flight" FAR, as well as beginning to look like a "commercial operator."
Not to mention that fact that very few flight schools, FBOs, or flying clubs will let you take a twin out by yourself with his kind of low time.
Its a great idea to get the rating, get the MEI, and then instruct wherever to get your multi hours, except for the fact that most flight schools reserve the "privilege" of instructing in the twins for the more senior, more experienced instructors (who all have decent multi time, and are thus "trustable" by the institution), unless you're talking about a place like ATP (which defeats the entire purpose of this argument with regard to cost savings). A second problem with that, is that while you obviously log the hours as an MEI, its not making you a better pilot from the standpoint of actually flying the plane. When you interview at an airline, cargo, or wherever you go, they want pilots who can fly and be trained to fly their equipment (as well as obviously having knowledge of FARs, etc).
That being said, I don't think you're going to find a way to pay for any less than 25 hours of Multi time, and yes, 50 is about the minimum where you're hire able these days (again, right or wrong).
Plenty of flight schools will let you pay for the rating, and then buy block time in the plane, for as many hours as you want.
With regard to the original question, as far as doing this for the lowest cost possible, I am not sure you really save money going the FBO route. Once you add up every flight hour and every hour of instruction you paid for, to come out equal to a program like ours (340 hours total, 150 multi (of which 50 are AATD), zero safety pilot time, unlimited instruction) I think you'd be hard pressed to get that kind of training out of an FBO for the same or less money.
Just my $.02