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Some of my rims can't take larger, but a couple can.
Are your rims 10mm wide or something?
I'd advised at least 25mm, or 28mm* if clearance on the bike allow it, it'll significantly reduced likelihood of puncture, last significantly longer, more comfortable and withstand pot holes.
Gatorskins are easy to get, 25mm is very common (but sold out quickly) in bicycles shop, they're not the most amazing tyres, but work really well for the general norms.
*old school rims with 13mm internal can cope with 28mm, it's only when you get bigger is when you lose the advantage of the tyres by needing to inflate it more than necessary to stop it squirming too much).
Are you limited to 23mm?