Listen to Jim.
If you want my humble opinion as someone who has done MMS and had some good success with it and is now a diehard 5/3/1 guy, DON'T MIX THESE PROGRAMS. Dan's program is very well thought out and is self-contained. That is, like 5/3/1 and Jim's supplemental routines, all the components are set up to compliment and feed into each other.
MMS has more than enough volume to beat the absolute crap out of you. The high rep squats are murder. I wouldn't toy with the program or add any more volume or weight than is already there. You're already going to be doing presses, lots of heavy doubles and triples on your bench, etc. There's really no need to try and tack anything on or think you can squeeze more out of it. The whole thing is set up around the high rep squats and eating more than you think you ought to.
MMS is designed to do a particular job: make you bigger. Hit it and quit it. Dan doesn't suggest you do it for long or all that often. On the other hand, 5/3/1 is a set of principles that can be used for long-term programming to suit a lot of different goals. It's a different sort of animal.
My advice: pick one and run it as written. Chart your results. Then run the other as written. Chart your results. Even then, I wouldn't start writing my own hybrid program from the two. But you'll be better prepared to make a choice as to where you might want to go next. As always, pick the right tool for the job and use it as intended.