Here in south western CT theres no limit. You get 2 either sex & 2 antlerless tags with your license & all the replacement antlerless tags you want. You bring in a doe & get a new tag. Last year every third doe you got a replacement either sex AND an antlerless tag, I imagine it'll be the same this year. I believe this is only along the shore. Inland counties get just the 2 either sex & 2 doe tags.
I shoot a bunch of does, dont see a problem if they dont go to waste. I gave 4 deer away last year & we ate 7.