What you're looking for is usually called Minimal Essential Medium or Eagle Medium. However there are many variations on MEM for various reasons. It's not necessarily sufficient for all mammalian cells, you should look to see if there are specific requirements for the type of cells you intend to grow, and almost all mammalian cells require the addition of fetal bovine serum to grow, which will be an undefined component.
For mammalian cells you can use any one of the commercial media available in the market (invitrogen ,gibco,himedia). I believe bacterial medium can't supplement all the essential factors required for the mammalian cells including the serum growth factors.
I know M9 can`t be used for mammalian cells. I was looking for something [maybe also a good receipt] to have a medium with all known components and to be able to change them as I want. I saw the MEM and I was thinking about using it plus supplementing it with what`s needed by my cells.