I modeled it out. It is certainly possible, but it will be difficult. The most important thing working in our favour is that somehow the EPL ended up with 8 teams in European competition this year (please someone tell me how they pulled that off?), either way, the result is that each point an EPL team earns is divided by 8. There are currently 6 EPL teams in the competition. Serie A on the other hand had 6 teams in the competition, and now has 5. Each point a Serie A team earns is divided by 6. As we go further into the tournament, each point for Serie A will go much further than one for the EPL.
A few other things that could help:
-Strong EL showing...If a team won it (Napoli I'd imagine) or if we had two teams in the final (Napoli, Fiorentina).
-Two teams in the knockouts...By qualifying in the knockouts you get 4+1 point...if Both Juventus and Roma got there, with Roma getting some easy initial matchups to help them get through a few rounds, and us going far irrespective of matchup (because we're actually good), that would also help a lot.
-More EPL choke jobs - a team finishing 4th in the group would be huge, but really I think only Arsenal has that risk...maybe City if Sevilla wipes the floor with them, and Gladbach win the final game. Obviously a team finishing 3rd would be mixed: they'd forgo the 4+1 reward for qualifying for the round of 16, but would have the full Europa league to earn points in. City in Europa would scare me to be perfectly honest.
If anyone is interested, I did build a model to calculate it...The main conclusion is that it will be a challenge (but doable) to get the spot next year, but the following year, Serie A is currently on track to get the spot back. The current coefficients for '16/17 are 51.58 and 51.16 for Serie A and the EPL respectively.
After scanning some of the above comments, I think a miracle scenario would be one where Arsenal finishes fourth, and the majority of the EPL teams exit the at round of 16. Meanwhile, Napoli wins the Europa League, and the other two perform well. In the UCL, if Roma perform well, and get past the round of 16 (by a miracle draw), and we get to at least the Semis...furthermore, dominance in the ties is important too...2 wins, instead of winning on goal differential also goes a long way. If a scenario even approaching this would occur, Serie A would not only have 4 spots next year, but have a nearly insurmountable lead for the EPL the following year.