Here is the thing, once you start conquering and colonizing worlds, you are essentially a major. The only paths to victory for a true minor would be tech or ascension, both of which would consist of optimizing one planet and hitting the turn button a lot. Go ahead and mod it in if you want, but it doesn't sound very fun to me.
If you could jump out to a large enough lead over the other major races, you could start producing colony ships for 1 or more of the minor races or give them planets and let them be a huge force in the game even though they wouldn't colonize.
I would hope they would allow them to invade planets although high in their tech tree with low priority unless other factors are met to give them a chance at conquest victory should certain factors play out.
One factor would be a galaxy with just enough systems created for there to be a system for every race major and minor making it that many races may only have 1 maybe 2 worlds for most of the early part of the game, give them a fighting chance if they stick around long enough....
Other options would be as mentioned in other posts make there a reason to keep them alive and not conquer them, say they would give you a good trade resource or production/research boost if you're allied with them versus just killing them off...
