My prediction on the next players to go from the 40-man as space is needed, updated in quasi-real time:

1. Evan Scribner: Right-handed relievers who can put up a 94 ERA+ with a 92 mph fastball are not exactly difficult to find. He's out of options, so he might well make the Opening Day bullpen, but he might also be discarded on the last day of spring training when some team tries to sneak a slightly better reliever (say, a right-hander who can put up an ERA+ of 96 with a 93 mph fastball) through waivers. There's no real reason to think Scribner is a diamond in the rough; he is what he is, and what he is doesn't add up to much.
2. Taylor Thompson: He's another righty reliever without a pedigree (44th round pick in 2009). He last started a game in 2009, in the Appalachian League. He's closed games in the minors and missed some bats, but 27-year-old relievers who walk 4.4 per nine in Triple-A don't usually transition well to the big leagues. He could figure something out in the spring and earn a job, but he could have done that with the White Sox, too, and they waived him.
3. Eury De La Rosa: He's a tiny lefty, which is adorable, but he only throws 90 with his four-seamer, and he's paid the price for his lack of stuff, giving up seven homers in 51 major league innings. He gets some strikeouts, didn't walk the world in Arizona (though he did in Reno) and is hardly a bad player, but there's not enough here to distinguish him.
4. Mark Canha: Listed mainly because he's a Rule 5 player. Honestly, he should probably be first, not last, because all it takes is a mediocre spring and he'll be headed back to ... uh, wherever he came from. I'm not looking this up. I'd like to think he can do a normal-sized human's version of Nate Freiman, with more versatility, but I don't think the A's are going to have a lot of tolerance if he doesn't hit lefties. They can feel pretty confident that Freiman will do that, so Canha's leash ought not to be very long.