Can you house a parakeet and another bird, like a cockateil togther?

Our parakeet is full grown but we’re not sure of his age since we found him flying outside. He loves his cage and never wants to come out, but he’s also so happy and talkative. However he seems scared of people and hasn’t bonded with either of us in 3 yrs. I can’t help but feel maybe he would like a companion.

Also we would like to adopt a bird from a shelter but worry it could give him an illness. Has anyone had a good/bad experience with adopting?

HOW to take care of a parakeet and a cockateil?

i just got 2 birds they were rescued…
cages were filthy.
they were being kept alive with moldy wild bird seed.
I cleaned their cages spotless.
I bought them new toys.and food.
they seem to be very happy , and are singing all the time.
I am TOTALLY bird stupid. is there anything i should know thats very important? I have never owned birds before. and I want to do right by them, they have been wronged for so long. I want to be the best bird mommy I can be. I am already a mommy of 3 boys, 2 cats, and 1 dog. Please if there is anything I need special for them please tell me. and I will get it.
- bratnumber5