It's certainly impossible with the current districts: even in the potential Clinton wave year some Democrats dream of, the absolute maximum for the Democrats in 2016 would be in ~ the 206-210 range (well short of 218), and they'd just lose many of those again in 2018.
I'm beginning to suspect that even in the 2020s, it'd take something drastic, probably including Puerto Rican statehood and five likely safe Dem seats, to really alter the math to a way that favors the Dems.
I actually think that PR would be a swing state with maybe a slight Republican lean (the politics on the island are very different than those of other Hispanic groups in the US). Also, the party that supports statehood is the more Conservative of the two Puerto Rican ones, so it would mean that it was having success. It might take a couple cycles to know for sure, but keep in mind that it was thought that Alaska would be Democratic, while Hawaii would be Republican.
