“with” is the preposition to be used in this case and I can’t think of an alternative that wouldn’t change the meaning of your sentence like “over” for instance.

• “keep you in touch over something”
• We can keep in touch over the Internet. What’s
• the point of not keeping in touch over years? If

I don’t like the preposition ” Keep in touch” I’ll just say that. I’ll just

have to remember and say no. But it’s a form.

We stay in touch “through” a medium of communication: the phone, email We may

also stay in touch “under” things of mutual concern or interest: a project

we’re working on (but better here would be “under”) We still stay in touch “after” a period of time: years, decades and sometimes, when

we don’t have time, through our sister whom we both see regularly.

We like to stay in touch for as long as possible about how that other is doing and I can

still stay in touch if I am going to die young in 2014 and happy after forty-four years.