The plasmids must have different origins of replication and different antibiotic resistance markers to be introduced into one cell. The promoters then should be able to drive expression of the downstream genes.

It is not very desirable to carry out a co-expression of proteins in the same host cell and this is even more true when the 2 plasmids carry identical origins of replication, risks creating an incompatibility between the plasmids and consequently the phenomenon of curing of these plasmids. However, the insertion on each of the plasmids of a different resistance cassette (for example Ampicillin on one and Neomycin on the other) while maintaining the selection pressure (addition of the 2 antibiotics in the culture medium) allows to maintain a certain stability of the level of expression of the 2 proteins (but not 100%, depending on other factors that can influence the expression and production of the proteins).

Assuming you can select for both plasmids separately (different resistances) then it should be fine. Both will be induced by IPTG induction assuming the strain is expressing sufficient lacI protein (otherwise it will be constitutive).

Even if the plasmids have the same origin you can co-transform them but you need to have different resistance elements to maintain selection for both of them.