Austin - as far as I know, a for-profit and a tax exempt entity CAN be a CG. Or I guess it is "Common Control" but has the same effect. See, for example, 1.414(c)-5.
But assuming they are not, I'm not aware of any reason they couldn't be a participating employer as a MEP, if your document allows it.
This is just off the cuff, from memory, so caveat emptor. I'd definitely have to spend some time doing some research before I'd venture a solid opinion on this.