Andromedans (from Star Fleet Battles) also use saucer-looking ships, IIRC.
Indeed they do, though in their case the "full" saucer is broken up in no small part by the placement of the warp engines:
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As it happens, there is a second known faction in the Star Fleet Universe which uses saucer-shaped ships: the Sigvirions of the Omega Octant.
There are a few differences between the Sigs and the Andromedans, in terms of their respective "saucer" designs.
In the case of the Andros, most of their ships are intended to deploy solely in open space; their larger Motherships typically have a built-in hangar bay capacity, from which they can use their advanced transporter technology to deploy or recover one or more of their smaller satellite ships as and when required. Although it is possible to park a Mothership in orbit of a target planet, and then beam a satellite ship (say, a cargo or commando variant) to or from its surface - thus bypassing the need for the latter to land or take off by itself.
Most Sigvirion ships, in contrast, are themselves designed to land directly onto the surface of habitable worlds. This is so that their crews - comprised of host bodies from a variety of susceptible species, each driven by a Sig viral intelligence - can spread the Sig virus to the locals on the surface. However, since there are all too many species out there in known space which are vulnerable to Sig infection, it's quite possible that a ship built by another faction might turn out to have a Sig-infested crew aboard...