I suspect Phoatu is going for something a bit more 'expansive' than just standard runner teams, or an association of hitmen like either the Smoker's Club or Chimera; he's looking at a large segment of the shadows being brought together. Even if they're not assembled into an actual organization, they'd at least be organized enough to say 'we can't hit that today, another one of our associated teams is working nearby'.
Phoatu, while
strictly speaking in canon such things don't exist in much of the Western World, it does to an extent exist in places such as Hong Kong - the
guanxi networks, complicated (and huge!) groups of people who know each other and have equally-complicated relationships (are they your social superior? financial inferior? etc.), which all tie into each other at multiple points. How you relate to your network, your standing amongst its primary and secondary members, and how it ties into other peoples' networks, makes for very compicated situations - but, if two teams are going after the same thing, may well result in the PCs having to decide whether or not to back away from the 'higher-
guanxi' team and hurt their professional relationship with the Johnson(s), or go after the thing anyhow and harm their
guanxi standing.
However, this is
your game; the only 'precedent' necessary is 'I want this to happen'. It's been guesstimated that there are between 60 and 90 'professional' SR teams in Seattle at any one time. It would be entirely possible for a notable portion of those teams, say 20 of them, to be gotten together by five or six fixers who specialize in different things.
if you have one fixer specializing in Japanacorps, one in organized crime, one in Matrix stuff, one in street-level and gang crap, one in heavy-hitter merc/force stuff, and one generalist, each of them is going to have their 'stable' of four or six teams who they can go to for work. By getting together, they can get access to a lot wider of a client base (the Johnsons), a lot bigger a resource base (the runners), and be able to actually have a group or two (or more) on standby or helping out in some other way.
Perhaps a Johnson wants a shipment hijacked. A Matrix team can be hired for overwatch, a standard team can be hired to actually acquire the goods, a street-level team can be hired to run interference with KE and nearby gangs, and a heavy-hitter team can be paid to be on-call and relatively nearby just in case the shit hits the fan. Nobody is going to walk away with the 70k the Johnson is paying for one night's work, but because the work is being spread around, the runners can handle a lot MORE work. You won't run once every couple of weeks, or once a month; you'll be in action every couple of nights, whether you're the lead, running interference, doing some tree-shaking, or just being on active standby.
This, gamewise, also lets you play around with different sorts of character sets. Have your players come up with several characters that'll fit in different teams - everyone has a hacker, a couple of combat sorts, a rigger or street racer, that sort of thing. Put together three or four teams for them to be, so they can pull their own fat out of the fire if it gets too hot.
