Can I go to MEPS for one service while in the DEP for another?

The deal is I was trying to join the Marine Corps for about a year and a half and they would not send me to MEPS to process my BUMED waiver because they had filled their quota of "qualified applicants" and didn't want to waste a spot on someone who needs a waiver. So finally I took my paperwork and went over to the Army and they processed me and got my waiver within the month and got me in the DEP a week later. Flash-forward two months and the Marines are calling me twice a day to get me to switch because they have had their poolees dropping out and being disqualified because of crimes and drug use. I want to join the Marines because it's a legacy for my family, but I don't want to leave Army DEP until I'm in the Marines DEP so they can't pull the whole give me a call back in a couple of weeks.