Found this construction problem from '83 and liked it. I don't know the best solution (yet), and maybe you can top it anyway.
Consider the (help) "game" 1.e4 a6 2.Bc4 a5 3.Qh5 a4. Now White can mate in two ways (and I doubt this value can be increased having 6 preceding half-moves). Maximize the number of possible White mates after 12 half-moves (which you choose).
