The events of Star Control II are part of a major galactic war between the established Ur-Quan Hierarchy and the atavist New Alliance of Free Stars. Several races are not aligned with either faction, but still interact with the members; there is no canonical term for these races.
The Druuge are shrewd businesspersons, first and foremost. They appear to have avoided Hierarchy membership by selling-out the neighbouring Burvixese while maintaining relations with the Utwig. The Captain can have a range of interaction with them, including slave trade, barter and war, but the Druuge remain well outside of both the Alliance and the Hierarchy.
The Melnorme are a transient and inevitably successful people who trade in advanced technology and intelligence. They can be a major help to the New Alliance without entering any formal agreements, and it was them who sold the ill-fated Probe to the Slylandro. There are no reported links between the Melnorme and the Hierarchy worlds. The Melnorme have no Sphere of Influence.
The Slylandro are a gaseous people who live extremely long lives and cannot leave their homeworld. They tell the The Captain about receiving friendly visits from the Precursors, the Ur-Quan and, more recently the Melnorme. The Slylandro have no Sphere of Influence.
The Spathi wanted to be slave shielded in order to follow a policy of isolationism and neutrality. Due to a communication error, they became Battle Thralls, but then defected to the New Alliance at their first opportunity and used the relationship to study the Slave Shield around Earth, which they replicated at Spathiwa.
(Optional) Neutral Worlds
Four worlds are free from the Hierarchy and will remain neutral unless the Captain invites them to join the New Alliance. These races did not participate in the Ur-Quan Slave War and were never incorporated into the Hierarchy.
Supox and Utwig
The Supox-Utwig Alliance is the only known pact outside of the Hierarchy and Alliance. Both worlds sit along the border of Ur-Quan space and if the Captain plays his cards right, both races will join the New Alliance simultaneously.
The Zoq-Fot-Pik homeworld is within Ur-Quan space, which poses a grave danger to this plurinational race. They seek contact with the Captain soon after the New Alliance is founded and, if they join, will send a delegation to the Earth Starbase. Regardless of their status vis-à-vis the Alliance, they will send an S.O.S. to the Starbase as their space comes under attack by Kohr-Ah forces. If the Captain is unable to respond within a limited amount of time of receiving the call for help, the Zoq-Fot-Pik will be exterminated before the Death March even begins.
Unofficial Alliance Members
Three races affiliate themselves tactically with the New Alliance but do not make their ships available for construction at the starbase. Because of this detail, many Humans do not consider them to be full members of the Alliance. Two of these races are not under the Hierarchy either.
The Arilou Lalee'lay were members of the original Alliance before disappearing in the final stages of the Slave War. In the late 2150s, they are (optionally) contacted by the Captain and provide aid to the Alliance. They send a delegation to the Earth Starbase like a full member but do not allow for the construction of their ships, choosing instead to donate a few vessels during their visit.
The Pkunk are at war with the Battle Thrall Ilwrath and will support the New Alliance even as they become heavily involved the in Yehat Revolution on the pro-Alliance side, but they do not formally enter into the Alliance nor the Hierarchy.
The Rebels are a faction of the Yehat torn between allegiance to their Queen and to their old Allies. The united Yehat were members of the original Alliance before defecting in 2234 to the Hierarchy and becoming Battle Thralls. They (might) eventually split into warring factions with the Royalists continuing as Battle Thralls and the Rebels supporting the Alliance without becoming full members.