Unfortunately this is not generally possible. You can get some intuition for why that's the case by considering, as an example, a two-dimensional decision space. The constraint you're asking for would look like "either I'm on the x-axis, or on the y-axis", which is not convex.

A formal proof would probably be something like: For a linear problem, the feasible region is convex, so if (x, 0) and (0, y) are feasible so too must (x/2, y/2) be.