Mobil 1 20w50 V-Twin (or any "V-Twin" marketed oil), for example, has nothing in it that would make it unsuitable for a wet clutch. Used it with great success and held grade in my inline 4 ZRX1200 with engine/cam/carb/exhaust upgrades (i.e. 145 hp/87lb-ft) on a 5,000 mile OCI. Gets hot on engine/oil temps at elevation in Colorado when going through any town or stop and go. Redline 20w50 dipped a bit in grade over 5,000 miles and currently SuperTech 20w50 V-Twin just went in to replace the Amsoil 20w50 V-Twin that went 5,360 miles. None of them lost shift feel and looking forward to posting the Amsoil 20w50 (got it from Pablo on this forum) analysis when Blackstone gets it done.
20w50 as a whole is more appropriate (for V-Twins and/or old air cooled Classic UJM's) given the temps air/oil cooled engines see during the riding season. I use 20w50 in the ZRX because the oil pressure at idle on the ZRX and that whole family of Kawasaki engines that spans decades has known low oil pressure when hot if running the recommended 10w40, despite liquid cooling.
EvoMan, The Harley clutch is bathed in oil, however it is not a shared sump with the engine oil which is what most folks think of as a wet clutch. That would be a distinction to note, IMO.