If your stallion is homozygous black he will always throw black based foals so a red mare would have a black foal provided there were no other factors in play. If she carries a hidden modifier gene such as the agouti(bay) gene then she can have a bay foal, the same is true of the silver gene. Since both agouti and silver act on black pigment only, you can't see either in a red horse. As said earlier you can't have a horse that is homozygous for frame but if it is homozygous for tobiano all the foals will be pintos. Most overo genes (frame, sabino and splash) can be expressed to a lesser or greater degree in any given foal and some horses carrying frame are solid or nearly solid visually and others that are nearly all white (maximum expression). Imo that is the reason they are so favored, the harder it is to get a color or pattern the more some people like it.
(big fan of frames here btw) Black based colours include, black, bay(black with agouti), buckskin(bay with cream), silver dapple (black with silver), silver bay (bay with silver), smokey black (black with cream), perlino ( bay with and 2 cream), and grulla/grullo(black with dun). If I missed any hopefully someone else will fill them in.
Hope that helps some.
ok so then what I am looking for would be a black and white homozygous tabiano? I have seen someone's stallion that was jet black along head and back 1/2 od him like someone drew Aline acrossed him colored him 1/2 black and 1/2 white is this his coloring ? can't remember if he had a totally black head I think so.