Hi Travis
The quick answer is “yes” you can protect the invention (based on the idea), and it (most likely) would be claimed in the patent application as a “method or process of doing something” which includes method steps of providing the product and specific steps of using it to carry out the process.

An example of a product with separate inventive applications is the little metal ring applied to: (1) a pig’s nose to discourage the pig from rooting under a fence and escaping from the pen…and (2)upolstered furniture or auto seats where fabric coverings are interconnected (e.g., backrest panel to a seat panel). Such fabric coverings will help protect your car seats from nasty frolicing escaped pigs. BTW, the same handtool is used for both “ringing the pigs” and covering seats. If you can think of a new use for the ring, you may patent that, as well.

Travis, my question for you is: what do you mean by a “new product with a different design?” Perhaps you’ve developed a new product which qualifies for a patent. ??