I took the general advice consensus and left things alone for now. I suspect the situation, or something similar, might come up again, and I thought I'd better give a bit more detail.
Eve is someone I see fairly frequently, as we walk our dogs on similar schedules. I would consider her a friend, even though I don't even know her surname. She's been to my house, I know a lot about her life and interests, and I get along with her really well. But since I have never met anyone in her family, and I have only known her for a couple of years, I would not claim to know her well. So, for all I know, she is a crack addict, ex-hooker, or professional shoplifter...things she wouldn't necessarily mention to a casual friend.
Similarly, I have known Adam for around 4 or 5 years, but really only as a chatty and friendly customer, so he again I know quite a bit about his work history, holidays, and views about a lot of things. But I don't know if he has a gambling habit, convictions for GBH, or a fetish for smelly sneakers.
The trouble when you get to your 40s is that it isn't all that easy to meet potential partners, so it just seems like a nice thing to do to help out a tiny bit. But I would never do anything more than just introduce people to each other. This would be much easier if both Adam and Eve were purely social contacts -- if, for instance, Adam was another local dog-walker, it would be a doddle.
Even if I did have parties, which I don't really, Adam wouldn't be someone who would normally be invited, even though he's someone I could imagine becoming friends with. From an etiquette POV, I should probably start a new thread in the Work folder, about if and how it is acceptable to cultivate a more personal friendship with a business contact.