Parakeets are flock birds, so it's a good idea to keep two or more in the same cage. How well the new kid gets along with others depends on the sex of your birds. He'll have to spend some time in quarantine, and more getting to know his new friends.
Sex of your Birds
Parakeets, also called budgies or budgerigars, behave a little differently according to their sex. Female parakeets are territorial, especially in small cages, so if you already have two female parakeets and would like another one, consider getting a larger cage. Male parakeets usually get along better with other males than females, as the females tend to boss them around. A pair of male parakeets should accept another male with little ruffling of feathers.
Quarantine
All new birds carry a small risk of disease, so it's important to follow proper quarantine procedures to protect your current pair. Keep the new bird in another room for the first three months, and care for him last in your daily feeding and cleaning routine. To minimize cross-contamination, wash your hands with soap and use different food and water containers, and toys, for different birds. Parakeets don't often show signs of disease clearly, so extending the quarantine period in case of doubt is fine.
Familiarization
Although parakeets love living in flocks, they also need time to get used to a new friend. When first introducing your new parakeet to your current pair, place the cages side by side so they become familiar with each other. Once any aggressive behavior has stopped, let the birds out of their cages together in the neutral territory of the room. Your pair should accept their new friend in their cage soon after, but watch for signs of bullying and repeat the above if necessary.
Breeding Pairs
Depending on the species, parakeets become ready to breed between 5 and 36 months of age. If you have a male and a female parakeet together, they may well become sexually active once they've reached maturity. Pairs of parakeets intent on breeding are at their most aggressive, so it would be unwise to try to introduce another bird if you suspect this may be the case.
References
Writer Bio
A graduate of Leeds University, Jenny Green completed Master of Arts in English literature in 1998 and has been writing about travel, gardening, science and pets since 2007. Green's work appears in Diva, Whole Life Times, Listverse, Earthtimes, Lamplight, Stupefying Stories and other websites and magazines.