Checking accounts and debt settlement

I have one checking with bofa that i am using for chase settlement.I have one more payment with them next month,however i also am trying to settle with juniper.Based on the lies i have been told by them so far(juniper) by telling me they will settle for such and such and then turning right around and saying something else i damn sure don't trust them one bit and i dang sure am not going to pay them by the same checking account as i am paying chase.If i did that they might drain it dry and then i could not pay chase the final payment thereby screwing that up.I have 2 with bofa and almost through with chase and they have kept their agreements but juniper is a whole nother animal i think.Anyway if i open another checking with bofa and use it for juniper if we ever come to terms could they in any way get into my other checking account with bofa and drain it?Thanks all