Have you quarantined the new male budgie?
If you haven't, it is best to start later than never. It would be best to keep the male in a different room than the females and let them have no contact for at least 30 days. Remember to wash hands before and after handling all budgies!
After the quarantine, I would suggest giving all three budgies an introductory. Let them play outside of the cage for a few days and watch how they interact. After a couple of days, if they do seem to get along well together, that's when you can house them together in a cage that's fit for the three of them.
Females will bicker with each other, but I'm not entirely sure if they were lessen that with a male around. If you find your females are still fighting, to a point where one is getting injured, it would be best to separate the females.