First, do you have a pic?
It can help to differentiate between crab grass and quack grass.
But for crabgrass, I think the best thing is the whole mow high trick. The
perennial grasses tend to quickly choke out crabgrass - especially the seeds.
Keep in mind that crabgrass is an annual that reseeds itself every year. So all of the tricks in killing baby seedlings are gonna be a big help.
I've just returned from three weeks of very advanced
permaculture training. Three weeks ago I might have hinted at this next
answer or just said nothing, but now I gotta say:
A) Have you considered a big, bushy perennial garden? Once you have a massive diversity of plants, such a trivial weed would be quickly ignored or easily mulched into oblivion.
B) Consider a lawn with 25 different species of things growing in it. You can still mow it once in a while, so it has that level look. But it will be loaded to the gills with all sorts of blossoms and fuzzy plants that feel good to the toes. Then, if there is any kind of weird grass or weed, it's just part of the diversity!