Can I Get a Crown with a Veneer?

I always evaluate the tooth before I come to a conclusion about what it needs. If a tooth needs protection I would do a crown for it, but if it is structurally sound, I would forego removing tooth unnecessarily and plan on doing a veneer. A good cosmetic dentist can make a crown or a veneer match an adjacent tooth or make a crown match an adjacent veneer.
I am quite conservative when it comes to removing tooth so I would always do what is best for the tooth. Some not do veneers because they prefer crowns. Whatever you do, I think you should save tooth structure and get a veneer if the tooth doesn't need a crown.

It looks like you want to put a crown on a veneer. It is absolutely impossible. The margins of the crown should lay down on a natural tooth, so it is better to remove the old veneer and then get a crown. If you want to get a crown on a tooth and get the veneer on adjacent tooth, it is possible.