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.
You new male is beautiful! It would be better to add two males to your flock after quarantine. The females may fight over one male and that would defeat your whole purpose for getting a male in the first place. I hear it can get pretty ugly especially when females go into breeding condition.
A note on quarantine..you need to have your new male not only in a separate cage , but also in a separate room from your existing flock..no contact for at least 30-45 days. You can click on the link in my signature to learn more about the importance of quarantining your birds.