As Clive says if you can get away with just one then that would be the easiest option as 55% solder is really the lowest melting of whats available to us now so the easiest to get to flow.
If you do want a higher temp one for the first heats then a 30% silver content one would give you a melting point that should not overlap, just take care not to distort any parts due to excess clamping pressure as the metal is starting to get a bit soft at the elevated temps. You will also want a flux that cane take the higher temps and longer time needed to get the work upto them such as HT5