How to manage join keyword phrase on Google search results

[Amateur]

Hi guys,

Is it possible to manage this problem?
I run a couple of websites and some of them have keyword phrase in domain name. And that's good, because i have managed to be placed on the first or the second page on Google. But, there is a catch.
Let's say that my domain name is (getsponsor.com), and my keyword phrase is " get sponsor", and let's say sponsor, sponsorship or something like that.
So, i have some traffic by this, let me say "joined phrase" -getsponsor.
Now, naturally, i would wont to be listed by "get sponsor", not only on "getsponsor". But, it seems that it's very hard to make Google to list you by the phrase you want to. Or there is some method that i am not aware of?
Can you help me to resolve this issue?

Thanks,

Mickey