I say go for it. Try different veggies. This way you will know for sure what works for you.

Ok thanks. I'll have to see what I can have brought in to increase depth.

If you let them sprawl as another option, water and fertilize appropriately, it might be fine. Sprawling plants take up a lot of space though.

PC

Raised beds seems like the best option to me.

I'd suggest that before you start building a raised bed a few inches over rock, you experiment a bit with drainage. If you irrigate that area heavily, do you end up with a pond? Is there good drainage? If not, and you you put a raised bed on top of it, you'll end up with a (largely underground) pond, which won't be good for roots. A raised bed over even clay can be more forgiving about drainage than a raised bed over rocks.

My beds are over caliche, and I have to remove enough of it to avoid creating a swimming pool.

Sounds like you're on a slope, which should be safe against ponding. That may mean that your raised bed will have the downslope wall higher than the upslope wall, but that should be OK. You may, as a result, have deeper soil on the downslope side of the bed. I would not recommend making the surface of your raised bed sloped.