Zinc competes with copper for absorption if I recall correctly, so the two must be kept in close balance. Too much of one can throw off the amount of the other in your body.
The effect of dietary zinc on intestinal copper absorption.
Inhibition of copper absorption by zinc.... [Biol Trace Elem Res. 1991] - PubMed - NCBI
Copper-Zinc Imbalance: Unrecognized Consequence of Plant-Based Diets and a Contributor to Chronic Fatigue - Weston A Price Foundation
So, increasing one can have an impact on proper absorption and utilization of the other. Probably not a huge issue for you, but t's something to keep in mind.