It can be a really bad idea for the sites. A bit of a gamble. I've seen several sites die as a result of an unbalanced collaboration... basically it can result in one community/site losing lots of members, especially if the sites largely overlap.
In fact I have never seen it work in a balanced way, there is always a net benefit to one site or the other.
A large part depends on the level of collaboration, and the type of collaboration. Mostly it depends on the sites themselves complimenting each other, not on competition. Really that will need my buy in and the owners of the other site, because the consequences are potentially extreme. For that to happen we will both need to be pursuaded of that benefit and prepared to gamble what has already been created. I am just being honest about my concerns with this. It can seem like a fun idea, or a way to create interaction, but someone pays the price, and it is usually one of the sites.
I appreciate that you probably want to do it for enjoyment and to support both sites, I am just highlighting that there is a very real potential cost. I've seen it kill many sites, so some care is needed.
That aside, the site staff (in particular) and many members, put loads into making this community thrive and grow. Songstuff is not a small site, and it has quite a lot of members, but it is neither a tiddler, not a giant leviathon, it is somewhere in the middle. It's still a lot to risk. So it would need a lot of work to put together, including a lot of effort to ensure that it is possible without damaging either site. Just now, I know that I personally don't have much if any time to put into this. Is it possible? Yes. Is it likely? The jury is out.
Worth discussing, maybe, but please don't think of it as a done deal.