You should not house multiple species together in a cage (in a MASSIVE, zoo-sized aviary, MAYBE). Even 2 birds of the same species often will fight and injure or kill the other...
Plus, you need time for each bird in the event that they don't get along (e.g., 3 hours each, minimum). Housing a trio is also generally a very bad idea.
Then there is the serious risk of symptomatic (but deadly) disease- hence the necessity for new birds of unfamiliar/non-cage mate birds in a persons house to be quarantined for 45 days (each as far from the other as possible--- rooms if necessary, but entire houses/building= safer (due to ventilation and dust transmission).
Unrelated suggestion-Read up on Teflon/PTFE/PFOA/PFCs- they are a big deal for future bird owners and have killed birds on different floors with temps as low as 350F.
Also, fumes, candles, standard cleaners, scented oils, wax warmers= very bad for them.
Oh-- and if you decide to construct an aviary, it is VERY important that you avoid galvanized things, zinc, nickle, lead etc...Stainless steel, aluminum in some cases (debatable), or some iron with bird-safe powder coating. Chicken wire and treated lumber (including the majority, which are sprayed for insects) can be deadly. Parrot will chew out of wood but can also be poisoned by it, plus it is impossible to clean properly when pooped upon.