Deadline reliever trade?

Oakland’s pitching staff is bullpen-heavy, and perhaps it wouldn’t be surprising if the A’s made the bullpen even heavier before Tuesday’s trade deadline.

With seemingly far more available relievers than starters on the market, the A’s would benefit from adding a bullpen arm to accompany closer Blake Treinen, rookie setup man Lou Trivino and Jeurys Familia, who was acquired July 21 from the Mets.

“We’ve already had a big addition that we’re really happy about, Familia, and he’s already been instrumental in three wins,” manager Bob Melvin said. “I try not to look too much into (the deadline). I don’t want to be disappointed. I like the roster that we have. If we don’t do anything else, I’m happy with it. If we do, then it’ll be a nice surprise.”

The Mariners, a team the A’s are chasing, added two relievers Monday: Zach Duke from the Twins and Adam Warren from the Yankees.

The A’s returned to the Coliseum on Monday after getting swept in Colorado, where the difference in the pitching staffs was on display. The Rockies rely on their starters to get deep into games. The A’s tend to go to the bullpen quicker.

Unless the starter is Sean Manaea, who’ll start Wednesday.

“It’s just the way the roster sets up,” Melvin said. “I’ve been happy with the way it’s going.”

The A’s scored just four runs in the three Colorado games, and the “semi-silver lining,” as Melvin called it, is that the back end of the bullpen got a rest entering the homestand.

Plus, the ’pen got deeper Monday when Ryan Dull was recalled from Triple-A Nashville. With three off days in the next week and a half, the A’s optioned starter Frankie Montas to Nashville and momentarily will go with a fourman rotation.

It’s Dull’s fourth stint with the A’s this season, and he’ll be on call with Toronto’s surplus of right-handed hitters. Briefly: Matt Joyce (lower back strain) had a setback — his back flared up when he swung a bat — and he was seeing Dr. Robert Watkins in Los Angeles on Monday . ... Jharel Cotton, in the clubhouse before the game, spoke optimistically about his rehab from Tommy John surgery after engaging in a round of sock throws, a big step in the long process . ... Cotton said he watches every A’s game and said of the recent comeback wins, “I was jumping up and down in my apartment. I think my neighbor called security on me.”