Inter breeding???

I think you mean inbreeding; it all depends on the history of the lines you are dealing with. If there is a long history of good health in a line there's no reason not to inbreed. that's how showers of fancy mousie maintain the purity of their lines. If you are dealing with petstore mousies, there's no way, usually to determine the health of the mousies, and it's best to avoid it if possible. This is especially true with any newer recessive varieties like rex, hairless, satin, etc., which are often hard to get at a petstore, but they do show up from time to time.

If you get meeces from a reputable breeder who can vouch for the soundness of the lines, or the lack thereof, then you'll be informed on how to prceed in making pairings.

I'll be back:

Respectfully, I must disagree with your statements.

Inbreeding is the correct term; linebreeding is another correct term. Whether you do either or neither is individual choice. I think you have overstated the degree to which either can be done without perils. Random mutations can occur at any time, and in captivity it's more likely to be a harmful thing than in nature where only those mutations that are beneficial and promote continuance of that line are passed on.

Looks like I didn't understand what you were trying to say. No worries.