Can something like a platonic relationship exist?
Yes and no. As everyone has pointed out, a “BFF” friendship is not possible, as it will cause feelings to develop.
However, there are multiple levels of relationship. I have a “working” relationship with many of my coworkers, both male & female. Such a relationship does not develop “feelings” (B’derech K’lal), as the guiding rule is to keep it business-like.
I think you can use the same idea here as well. If there are ground rules, and you (both) agree not to attempt to develop the relationship into something else, then you can move forward. Otherwise, watch out.
Hatzlacha either way. You are in a tough situation.