I think if you are prepared to put the work in, then it can work - many people have multiple dogs.
It is a huge commitment in terms of time, space, exercise requirements - and most especially making enough individual time for each dog for training, one to one cuddles, grooming etc.
It's also a huge financial commitment - food, vet bills, insurance, necessary items such as collars, leads, toys
- and with a Bichon - grooming.
I would write that all down and make sure you are prepared to commit before taking on another dog. With each additional dog you add you will see more pack behaviour - so that is something to be prepared for too.
How are your dogs with other dogs? Are any of them elderly and would therefore find a pup difficult and stressful?
Is someone at home most of the time?
Lots to think about!!!Also with a Bichon, many breeders say not to let them off lead as other dogs are quite prone to attacking them - think small, white and fluffy.