Here in southwestern Montana the Lesser Goldfinches are very rare, though I have observed a migrating male at the feeders and baths in October 2023. We have flocks of up to 20 American Goldfinches at a time in winter though they also leave when they get there breeding plumage, and then start coming again in late July or Early August, though at sunflowers, not feeders. I don't discourage any birds and let House Sparrow, Collared Doves, Grackle, and Starlings come at their own free will. We've had the House Finches nest as well, though they only had their first brood at our feeders. Here is a clip of the molting male goldfinch.