Answered[ Edited ]
You can absolutely use the Laura Mercier Mineral Primer with your HD foundation. I would suggest that if you have oilier skin that you may want to try a different primer that may be less shiney and less of a sheen as well. While the Laura Mercier primer is smoothing and softening, an oil free or mattifying formula may be your best option.
Laura Mercier Oil Free Primer
Sephora Collection Anti Shine Foundation Primer
You can also just use a hydrating primer which is softening and smoothing too and great if you happen to have dry skin:
Stila Hydrating Oil Free
I suggest these primers since the MUFE HD foundation can be more shine inducing and leave you with a glowing complexion.