Keen on vs keen to

I would use keen on doing when talking about my general likes, and keen to do when talking about a specific instance, so

I am very keen on swimming

I am very keen to go swimming today

But the difference is subtle, and I don't know that everybody else would make that distinction.

The third one is possible, but a little unlikely, because keen that is usually talking about something happening that depends on other people's actions (possibly one's own actions as well), so it sounds a bit odd when talking about one's own ability to do something. I would expect it to imply that somebody else must do something to make it possible for me to do the thing, so

I am very keen that I can go swimming today

suggests that I need somebody to take me, or people to leave me alone to get all my work done first, or the doctor to pronounce me fit to got swimming or something like these.