word choice - "Ideas on" vs. "ideas for"

I'd like to know when to use "ideas on" and "ideas for". I think these are correct:

• I'd like some ideas on how to improve my team.


• I'd like some ideas for improving my team.



• I have some ideas on that subject.

This feels less correct to me:

I'd like some ideas for how to improve my team.

This feels plain wrong:

I have some ideas for that subject.

However, I don't know why. Which phrase should I use, and when?

Edit: I'm specifically interested in the grammar breakdown — is that last one wrong because it's a noun? What about "how" — how does this change it? What are the rules?

Answer

Cambridge Dictionary Online suggests these proposition for "idea":

If you have any ideas for what I could buy Jack, let me know.

That's when I first had the idea of start ing (= planned to start) my own business.

And about your example:

I'd like some ideas for how to improve my team.

sounds odd and wrong.
After "for" a ing-clause is used and after "on" a relative-clause.

Ideas on what to eat to night

Ideas on how to learn

Ideas on where to go

And

Ideas for eating

Ideas for living