Q. Do Cockatiels and Parakeets get along well enough to live in the same cage?
A. Budgies and Cockatiels can get along but it depends on the individual bird. After proper quarantine, you can start with putting them in separate cages side by side so that they can get used to each other. After a minimum of a week with them side by side you can see how they get along out together in neutral territory (on a play gym or on your finger together). If they seem to get along OK, you can then try them in the same cage, but make sure you watch them very carefully the first couple of days and separate them if you see any quarrels. It is rare for tiels and budgies to fight, but if they do they can really hurt each other so make sure that when you put them together it is during a time (maybe a weekend?) when you can monitor them well for the first couple of days.
Ironically, it is usually the budgie that gets feisty with the Cockatiel if anything. Budgies tend to be more aggressive than tiels, despite their smaller size. Also, make sure that you have plenty of food and water bowls for the birds. If you have two birds, it is good to have two food and water bowls, if you have three birds, try to have three food bowls and two water bowls, etc. This will minimize the concern that one bird will "hoard" the food and/or water. Sometimes, the birds will not necessarily fight, but one will keep the other from food or water. Birds are like people in that some get along and some just don't It is just going to be important to monitor them closely in the beginning.