I have asked myself (not tested) if it is possible to integrate both bootstrap and materializecss into the same project
Since both frameworks are for the same purpos
I added Materialize to my bootstrap website and it worked fine, like JC Borlagdan said though there is some overlapping. I just use a website inspector and (usually right click > inspect element) then just turn off the bootstrap or materialize property to see which one I like more and remove the styling from the one I don't like. Just make sure you get the non minified versions of materialize and bootstrap.