Thorne makes some good multi-mineral formulas.
http://www.thorne.com/Products/Minerals/Multi_Minerals/prd~M250.jsp
For systemic enzymes, Wobenzym and Vitalzym are considered to be quality products.
Regarding minerals, the body doesn't lower the production of them because our bodies don't produce them. We NEED minerals. I would even go so far as to say that minerals are more important than vitamins, and that mineral deficiency is one of the main reasons for the plethora of modern disease.
As for enzymes, I don't think anybody really knows if exogenous supplementation reduces our body's own production. Personally, I think it's possible, but production should normalize after stopping the supplements.