You get basic access to them all during the campaign, but after that you have to make a choice and stick with it.
No completing contracts for rival syndicates, no access to rival syndicate abilities, no changing teams.
Who would you pick?
[spoiler]It’s The Pikers for me.[/spoiler]
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Bungie has being doing away with us having to "chose" for years. Mods used to be tide to specific elements. Grenades were tide to specific classes. We had pick a single element to play. I think that the long term goal of some designer is to dissolve character classes. I favor of pool of abilities that select only a limited a set of, along with our asthetics.