Yes you could move them to a new tank but you would have to cycle it again, as you can't use anything from the tank they are in, as the gravel or sand wan't throwing away, plus the plants, filter sponges wan't replacing i wouldn't even bother sterlising them, plus filter would want sterlising along time in a bucket of hot salty water running, then rinse in clean water again with the filter running, and let it dry out for a couple of days, same procedure with cleaning the tank.
Plus only healthy fish which you think have no signs of desease should be moved to the other tank, if you suspect a fish might have desease, don't bother transferring it as it will of just been a waste of time.
Mothing special just a housewife with two grown up children, and spare time on my hands.