The mini draws like 350W overclocked. You can likely run three of them on one APW3++ (though it's rated for only 1000W @110, I've never had a problem going over with any of mine--not suggesting others do it, just saying).
More like 420 watts at 750 MHz using a single Bitmain APW3+++ per Mini.
Mine peaks hashrate-wise at 718MHz, and draws around 350-360 according to my kill-o-watt. Are you on 110-130v or 220-250?
Even at 420, you can safely run two on one APW3++ (as long as you have enough room on the line). 3 is a risk, but two should still come in under the max (unless you're on 220, in which case you could really run 4 if you add more cables).
EDIT--to run three you also would have to add two cables, my bad.