There's nothing stopping that from happening in my proposed plan of all the individual <insert name here> HLP orgs being part of a massive alliance centering on <main HLP org>.
The link The E posted mentions that some orgs may only allow you to join allied orgs, so that means there's clearly organization alliances. Using alliances, we can have a centralized, nondescript, and general HLP org everyone is part of while people who want to can go set up their own HLP-aligned organizations based around whatever, like an Alpha 1 cult or the potentially very divisive BP-inspired ones like Serkr Team, the Wargods, and the Gaian Effort, and since everyone is hopefully part of the main HLP org, we can all organize stuff there, for example Bosch Beer Trading hiring some Gaian Effort mercenaries for a convoy escort.