Can you paint eggshell latex paint over a latex high gloss paint?

Painting over just about any sheen is possible. The only thing that I would recommend is to primer the surface 1st for a better application of the eggshell. If you do not primer the surface there may be a chance that the high gloss will show through and end up costing you more money to apply the much more expensive eggshell instead of the inexpensive primer. Unless you have plenty of paint for a second application of the eggshell. Then that would be okay. I do believe you can cover any sheen ( depending on color ) with two coats.