Another twist is to require some combined scores. E.g. for a two-man team, you need 6 A scores, 6 B scores, and 6 AB scores. When mixing single and combined scores, you have to use score relative to par as a basis, not simple net score, or otherwise, you'd always pick a combined score for par 3s.
Yet another possibility: for 2-man teams, use one score per hole, to be chosen immediately after the hole is played, but no more than two in a row from either player (Two-and-Thru). For 3-man teams, use 2 out of 3, and the unused player must be used next hole (3rd man In). In either of these formats, if all team players score better than net par, you take their combined score (total scoring relative to par, of course) and no constraints on next hole.