No, definitely do not introduce another bird to a cage with a breeding pair! Lovebirds can be very territorial and even more so when they are breeding. You can only have one pair in the cage when breeding. It doesn’t matter how well they may get along out of the cage. Once another bird “invades” a breeding pair’s nesting area, the pair will most likely kill it. The females are the most aggressive and sister or not, the breeding hen will kill the invading hen. Even if by some rare chance she didn’t, you can’t have one male trying to breed with two hens and trying to help both care for eggs and chicks. It would be too exhausting and most likely he would give up and none of the eggs would hatch or none of the chicks would survive with just the females trying to do it
Also, birds have no concept of being related once they are grown. This is why related birds should not share the same cage if they are opposite sexes. They will breed and the chicks will have issues from being inbred. So if your male and female breeding pair are related, then you need to throw away the eggs and take down the nest box. I only say this since you mentioned having sisters. If the mate doesn’t return, then you would need to find another bird about the same age for your single female.
Thank you for asking Lafeber,