You will need a different milking machine set up for each of these species both wrt pulsating speed, vacuum, streng5h and the cluster obviously as well.
So if you need to switch to a milking machine, then one species to be milked only is the only choice IMO, given that a good quality 2nd had machine is still near enough 1k....
And if equipment etc is the issue, goats are the best choice wrt milk quantities, ease of handling and kind of kit required. bTB may also steer you towards goats rather than cows. Sheep are (as far as I know) very seasonal and unlikely to run through.