There are no "rules" for multi-player BT (AFAIK), but they tend to fall into the following categories:
Free-for-all: three or more sides each with their own agenda facing off against everybody else. (played one of these with double [triple?] blind rules... GM nearly had a conniption...
Teams: works best with even numbers, but can also work as 1 v. 2 or 2 v. 3+, where each side has the same agenda and is facing the opposing team.
Gangbang: one veteran player v. 2+ opponents; different from "teams" in the comparative experience of the players
Multi-point; works best with five players (each representing its own house, clan, group or interest); can be done "BT" style: 5 houses; each is opposed by the two flanking houses [i.e. Liao is opposed by Davion & Marik], while the other two houses are its nominal allies [in the Liao example, Steiner and Kurita are its not-enemies] or it can be played M:tG style: the two players/factions next to each player are its allies and the two across the table its enemies. A GM is pretty much mandatory for a smooth game; works best when each player/faction has its own victory conditions.
High-Low: one pair of players takes care of the air war, the other pair the ground war... as a variation: one player controls one side's air and ground forces, while another controls the opposition's aerospace forces and the remaining player the opposing ground forces (heck; a third player could handle a wet navy battle!). For the truly adventurous, have a non-wargamer play a monopoly game simultaneously... using 'mech minis as tokens, of course. :D