Can you have e-mail hosting and web hosting on the same domain with two different providers?

I currently have Microsoft Exchange e-mail hosting with 1&1 on my domain, and I would like to add a full site and e-commerce store using the same domain. However, I don't care for 1&1's e-commerce/web hosting proposition and would like to take a competitors service. Is it technically possible to do this, or would I have conflicting DNS nameservers?