You absolutely should be able to fit all 3. Install your flip up BUIS as far back on the upper receiver as you can and you should have plenty of room to fit a magnifier and the Eotech no problem. Most magnifiers are built to mount a little farther forward and to flip up over the BUIS to save a little room.
This is not my rifle, but one of the first pics that popped up on Google. It has an A2 front post, but it gives you the general idea.
I'm not the hugest magnifier fan, but I was helping a younger vet on my range last week zero his rifle and new red dot with the exact set up. He loved the Eotech and thus decided on the dot and magnifier with his flip up BUIS. For me, it's just too crowded and too much weight when you can opt for a 1x4 scope and achieve pretty much the same thing. I will say though that I do like the Eotech reticle.
Sounds like you have not shot your OR yet. Good luck with her. Get the BUIS first and get to the range before deciding on the red dot set up, that's my opinion.