I doubt that you can get a partner for just one in

I doubt that you can get a partner for just one indication. No company is going to want to advertise a drug and then have some other company use it for additional indications -- while the partner gets nothing.

For example: Viagra now appears possibly to be beneficial against Alzheimer's. (I have my doubts about this, but let's pretend it really does work against Alz.)

Let's say (not true, just using for example) that Viagra was a joint venture with a smaller company. Would the Big Pharma that made Viagra a household name be happy about the smaller company getting ALL the profits from its use for Alzheimer's?

A partner is going to want to have a piece of ALL indications. They can structure something like a right-of-first-refusal for other indications, and set up parameters for profit-sharing.