Agree with Gooselee that Reserve is the best option. However, to answer your question, yes, you can pay to upgrade a companion ticket, I've done it before. It does not usually result in any great deal, especially when you factor in the annual fee, but it will probably be slightly less than paying for two tickets. It is sometimes better to call in and ask an agent to do it then to accept the offers online, which are often inflated. You will usually be transferred to the promotions desk, as they are supposed to handle this.

Note that you don't get "credit" for the companion ticket, and the pricing they come up with is confusing to me. What I mean by is that you don't just pay the difference between Y and C+ as though you have paid for two Y tickets, but the price also does not seem to be like a whole new C+ ticket for the companion either, so they must have some special pricing for these situations.