Restricting Coupon Codes

Does anyone know if there is a way to keep customers from combining coupon codes? We want to set multiple coupon codes, but we don't want our customers to be able to combine codes for a double discount. If a customer uses a 10% code, we do not want them to also use a 20% off code to an already discounted item.

This depends on how you set external variables.
In general, you want only ONE external variable to have Show in cart as coupon code set to YES, and apply your rules to it only.
The only way users could use a double code is if you have 2 or more variables shown as coupon codes: but in this case, the fact they can use 2 codes is exactly the behavior you asked for with your setup

Resurrecting this topic. I think the issue here is there may be ongoing codes offered such as an industry discount, and a sale discount offered simultaneously for one product. You don't want to restrict your industry discount just because you are offering everyone else a discount for one product. In this situation you have to have two variables showing at once.

Can there be added a way to accept both codes into one variable presentation into the cart? It looks complicated to me from all view points, but would be nice.

It would actually be very hard, but for the reasons explained in he original post I'm not understanding how this would be a good idea.
If you could have inputs for more codes, then what should happen in the event a user uses them all? Apply a double discount?

That is the point of bringing this up. Two codes give double discount, so do not want that. So then, how could we offer a permanent ongoing discount to certain customers and offer a sale discount too? It's impossible.