Will HOF vote for more than 3 next year?

I think it unlikely. As you said, it's seldom they even induct three in a year, let alone four. Certainly there are more than three who deserve to be in the Hall, but with the crowded field and the 75% threshold, three is the max I can see. The three I most expect are Maddux, Glavine and Biggio with Frank Thomas getting in a few years down the road. Jack Morris won't make it. He'll be no higher than the fifth best pitcher one the ballot. The others you mentioned (Bagwell, Kent, Piazza, and Raines) are no guarantees. Kent in particular never struck me as a Hall of Famer. Bagwell and Piazza have solid chances. Raines might make it, but it'll take him at least five years to accumulate the votes.

Lots of talent even without the players with PED questions. It's going to be nice and deep for the next several years. But I don't see the four mark being reached.

One, for sure! Greg Maddux.

Biggio? Maybe.

Piazza? Maybe.

The rest? Who knows?

Maddux and Glavine get in.

Thomas should get in, and I think Biggio can get enough votes to flop in his favor next year. He was close this year, and deserves to get in.