I often brew a small beer from the second runnings of a big beer. I'd say just take what you get and have fun with it. From an imperial porter, you might get something like a mild. IME it's always been 3 or 4 gallons of ~1.020-25 wort that ferments way too dry and is of lesser quality. But it's free(ish) so why not?
Things I have done to compensate:
Collect less, and stronger 2nd runnings.
Add sugar to bump the gravity. Keep it cheap!
Add DME. This is obvious but it's expensive and you may not want to use much in the second runnings from a dark beer as the results might not be to your liking.
Use more base malt in the grist but try to hit your starting gravity, thus leaving more sugars for the small beer.
Add more malt to the grist and do a second mash at higher temperature.
Use maltodextrin to combat the low finishing gravity.
Steep specialty malts to give it more body and character.
Use a less attenuative yeast.
Traditionally I think the late hops from the first beer were used to bitter the small beer. Cheap.
Or go for something hoppy! Use the opportunity to try out a new hop.
I have also added a small amount of lactic acid, cacl or gypsum depending on the beer.Www.braukaiser.com
has a parti gyle simulator. http://braukaiser.com/wiki/index.php?title=Batch_Sparge_and_Party_Gyle_Simulator
That may be helpful.
Have fun with it!