I would say go and get Carlos Santana or JD Martinez and add to a good but not great (yet) offense if not for the Sano Q mark. The reality is that the team needs to hold open the DH spot for 40+ games of Sano and I don't think you can sign (for significant money) a full time DH. Yes, Santana could bump Mauer from the lineup or JD could bump an OF'er from the lineup but I don't think that is a good option if Sano needs extended DH time.
DH next year
Sano 40 games (a big unknown with his injury)
Grossman 60+ games
Rosario/Kepler 10 games
Garver 10 games
Mauer 10 games
Escobar 10 games
22 games leftover for the above mix of players
Vargas could be a factor but I don't know you can make a bench of Garver, Grossman, Escobar, Adrianza and Vargas work for an extended period of time. All but Adrianza is potentially a better hitter than Vargas (not terrible at hitting) while adding a lot more positional versatility.