Is it possible to switch between Ph.D. departments at the same university? I recently asked about the ethicality of staying in a Ph.D. program (first-year) while attempting to transfer to a different university that I had declined previously. Unfortunately, the funding was cut short for said program and I did not get off the wait list for funding. 

The main reason I wanted to transfer was due to the fact that I wanted to focus on a more applied math program as opposed to the current program I am in that focuses on bioinformatics/biology. Since the transfer/funding did not work out, I was curious if I could possibly transfer from the Ph.D. I am currently in to the math Ph.D. program. They are both under the same college of sciences.  I did my undergrad in both math and cell/molecular biology and I believed I could incorporate enough math but if possible I’d like to just get the applied math Ph.D. and apply it to biology instead of the other way around.   

My two options are either to stay in my program and recruit many math committee members or to outright move to the math department. I don’t particularly want to ask my own department yet because I don’t want to be looked down upon or lose any funding because I do want to stay here and will happily finish (eventually) by incorporating more math based individuals.

I was wondering if this has been done before or if anyone has any advice on how to go about this? Obviously I’d like my funding to carry over and I believe since they’re in the same college of sciences it may be doable. I’m worried that I’ll be criticized or judged for wanting to do this or lose my funding. Since my first option of going to the other program at a different university didn’t workout and I didn’t hear about it till a week ago, I was unable to really follow this second option.
Whether it can be done or not depends entirely on the regulations of your particular institution. What is much more likely to say is that you will probably not be able to carry your funding over from your old department to your new one. Funding very rarely can be transferred, since it is usually attached to some project or department, rather than any individual.