For other textiles, some people have food luck with lemon juice and let it sit in the sun for a while. I've never tried it so don't know if it will lift the stains. The juice would be acidic, though, so well suited for protein fibers.

Any idea if the stains are food or grease related? If I didn't want to pay the dry cleaners, I would be tempted to spot treat with liquid Dawn dish detergent ( regular formula ) or a liquid laundry detergent that has some enzymes.

Thank you so much for the reply, Cavimum.
As for the stains, they are most likely in the food/coffee/oil family. And they definitely developed over time - we had been living without a washer, so all the visibly clean sweaters went into storage without getting washed beforehand (bad idea, I know). I would have hand washed them had I seen the stains, so I'm assuming they are pretty set and "fermented" by now, yuck.

I wonder if enzymes would be worse for the fabric than percarbonate?.. In all honesty none of the sweaters are very expensive or special, so I just might give it a try and see. I'm sure a one-off won't do too much harm, but I'm also curious if percarbonate can be used on a semi-regular basis on items such as wool socks, which don't always get clean with a mild detergent.