Trojie occasionally gets suborned into helping out with other departments - she's definitely either volunteered for, been pressganged into or simply refused to leave missions belonging to the Department of Angst, Department of Mary Sues and Department of Floaters. But she's never actually changed her Department.

Basically you can pretty much switch your agents round departments as much as you like within reason, although some of the smaller departments (WTF, FicPsych, and a few others) operate under the auspices of one particular Boarder and they might like you to ask before you throw your Agent into their sandpit, as it is.