I know you're talking about recent years, but here are some stats.
Number of players in the Open Era with at least three Slam finals: 38
Active players with at least three Slam finals: 7 (Federer 31, Nadal 27, Djokovic 26, Murray 11, Wawrinka 3, Cilic 3, Thiem 3)
Players with 3+ Slam finals and no titles: 1 (Tony Roche 3)
So you're right, no one else has done it recently - not Tsonga, Berdych, Ferrer, Nishikori, Raonic, all of whom only reached one Final (so far). Kevin Anderson reached two, as did del Potro.
From Roger's generation, Ferrero reached 3 finals, Hewitt and Safin 4 each, Roddick 5. Going back a bit further, you have players like Kuerten, Kafelnikov, Rafter, Bruguera, Ivanisevic, Chang, etc, reaching 3+.