Difficult to find a budget integrated amplifier that will effectively drive 2 pairs of speakers at the same time. Both speaker pairs would have to be 8ohms or better across the frequency range. Few are. Many would have connections for 2 speaker pairs with a selector that would allow you to choose a speaker pair to listen to individually. My cambridge Audio 540C will allow this. I would not rum 2 pairs at the same time however.
If an integrated has pre outs you could run additional amplifier to the 2 pair of speakers. If the additional amp has gain controls you could then adjust the output of the 2nd speaker pair relative to the 1st pair.
If an integrated has pre outs you could run additional amplifier to the 2 pair of speakers. If the additional amp has gain controls you could then adjust the output of the 2nd speaker pair relative to the 1st pair.