Can you put latex primer under latex paint?

In most cases yes.

Primer is applied according to what it is going on, not what is going over it.

- Latex / acrylic / water-based primers are good over drywall, stucco, brick, patches and repairs made with polyfil or other drywall patching compounds, paper, and many other porous materials. Once the primer is applied and dry any type of paint may be painted over it.