Still on Hazen's to-do list is adding another reliever, possibly another catcher and a left-handed hitter.
"We like some of our internal options," Hazen said of the bullpen. "We're trying to build out as much depth to the bullpen as possible and we're open-minded. However, we can get outs."
With a surplus of starting pitchers, it's possible the D-backs could shift one or more of the starters to the bullpen, giving the club a valuable multi-inning weapon. That is not likely to be something the D-backs decide to do until well into Spring Training.
"At some point we'll have to make that decision," Hazen said. "We have a long way to go between now and then, before we have to do that."
After non-tendering catcher Welington Castillo, the D-backs signed Mathis, who is well-regarded as a pitch-framer and for his handling of a pitching staff, to go with Chris Herrmann. The D-backs also claimed catcher Juan Graterol off waivers in December.
"We liked [Graterol's] defense. Our scouts really liked his ability to receive, so we're excited to get him," Hazen said.
The D-backs are still keeping their options open when it comes to adding more catching. Herrmann's ability to play all three outfield positions as well as both corner infield spots gives the D-backs flexibility in how they handle the duties behind the plate.
So, Arizona could acquire another catcher to split time with Mathis and Herrmann, or it could acquire someone who plays the position on more of a full-time basis.
One name to keep an eye on is free agent Matt Wieters, whose market hasn't materialized the way he probably hoped. Whether the D-backs could afford him, though, remains to be seen.
Steve Gilbert has covered the D-backs for MLB.com since 2001. Follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.