Together for?

The context below says "the only possibility at the moment would be a fellowship", so "we" suggest (think about) that you write an application for the fellowship". The question is that I failed to understand the use of the word "together" - together with what? An application for a fellowship, and then you together with the fellowship? It could not hold water. Maybe a DAAD fellowship is another fellowship. So "we" have suggested you to apply two fellowships?

Context:

thank you very much for your interest in an MD at our department. Your research background would fit with several studies we are currently working on.
Unfortunately, we do not have an open position at the moment. You said that travel and living expenses are covered by a grant, but I guess you would still need a regular salary, right? In this case, the only possibility at the moment would be a fellowship. We can think about writing an application together for example for a DAAD fellowship. These fellowships are only for up to 10 months, but could be a starting point.