Hi Reesa,
I was in exactly the same position some time ago. A client's competitor did approach us to redo his site after seeing what we did with my clients site. I called my client and spoke to him about it and asked if he had any objection to us undertaking the work. He was initially reluctant, but after just a few minutes of chatting he came to realise that his competitor was going to get the work done anyway, if not through us then someone else. Not only did he agree, but he later told me that he was very pleased that I had called and spoken to him first, as it showed loyalty on my part towards my existing clients. The new client also asked me during the development how my original client felt about our working for him, and when I told him that we had spoken to him prior to accepting the job, he seemed pleasantly surprised.
Since then we have gotten additional work from both clients.
I agree with Lori though, that
SEO is a different ball game altogether.
All the best
Vik