Do you mind me asking what size your cages are for your hams and mice? The capacity (i.e. no of litres a bin holds) doesn't let you know the actual floorspace. I know you let your animals out every evening for hours at a time but big enclosures with lots of floor space mean that the animals can have loads of fun running around for the hours during the night when no one is with them (I worked out that one day in a mouses life is the equivalent to around 2 months of a human year, so even 2 hours in a cage can seem like weeks to a mouse.) Your existing cages can always be added on to any new cages to make ham and meece mansions - I found Ikea really good for big boxes. The large Samla one cost me ÂŁ22 and it's the same size as the big hamster heaven cage

It's also something to consider if you do decide to breed as given the number of babies you could potentially end up keeping you may not be able to give each animal the same amount of free ranging time as before if you ended up keeping several litters worth of babies.
Have you decided if it is your mice or your hamsters you are going to breed? You only posted about breeding mice last week. It might be better for you to decide on one, learn all the genetics and good breeding practices of that species before taking on the challenges of breeding both at the same time when you have so much to learn - especially as breeding both at the same time would mean a lot more cages of a decent size and a lot more animals that you could end up keeping on top of having to learn all the genetics and inheritable problems that you need to avoid breeding.
To add - I don't know any rescue that would let you take an animal if you were breeding. And if a rescue did let some one who breeds take a rescue in, I have to admit I'd avoid them with a barge pole, I wouldn't want to go to a rescue knowing they would let a breeder take in an animal and it could be used for breeding (as I very much doubt they would be honest about their intentions of doing it either. )