Haha, I totally get what you mean!

Until recently, I would have been tempted to say no. But during the conversation he had at the start of Journey to a NU World, I actually think Dante was looking for a collar for Sooley! It's not confirmed or anything, it's just a hunch. Blade mentioned spikes too and I could see Dante agreeing with him, but his reason would be that a spiked collar could keep Sooley safer while he hunts in the desert (and not that the collar needs to be spikey like him, omg. Blade PLEASE).

So overall, I think Dante doesn't have outfits for Sooley but he could have accessories that serve a specific purpose.

For instance, @t_torry drew Sooley in a little raincoat once and it was so freaking cute ;; I can see that happening, I see the vision.

Exceptions would be accessories for special occasions (like a wedding maybe 👀 ? A corsage on a collar~).

Your question made me think that I'd like to see Eiden try to sneak a ribbon on Sooley, but he's still too scared of the leoger to pull it off. Dante could walk in, confiscate the offending ribbon and ask Eiden to leave. He'd grumble about Eiden not showing Sooley the respect he's due... until he wonders what could possibly be the appeal. Curiosity gets the better of him.
Sooley doesn't flinch when Dante ties the ribbon around his neck. He just stares at his master blankly. And, just for a few seconds, Dante gets it. He really, really does.
But he shouldn't give into the temptation of treating his powerful, well-trained pet like a common house cat, as adorable as he may be.
He immediately unties the ribbon and swears to never do it again.

(Thank you for asking! :3)