Can “itch” be a transitive verb, i.e., can an itch be itched?

Can itch be used as a transitive verb? In other words, can you itch an itch as you would scratch an itch? Dictionaries differ, with the bigger hitters saying no. Are they bearing the proper standard or just playing it conservative?

You'll have to explain what you mean by "proper standard" — but, no, what the "bigger hitters" (again, what are these?) are doing is waiting until a usage is far-reaching enough for them to bother to document it. I guess that's what you'd call playing it conservative.

That said, what one does to an itch is scratch it. Something can itch (intransitive) all by itself, or be itchy, but itching an itch feels like a bizarre usage to me. I'd be curious to know what dictionaries endorse that use.

NOAD, for example, lists only an intransitive form:

itch verb [intrans.] be the site of or cause an itch : the bite itched like crazy.

Addendum I answered this nine years ago, but since then I've recognized that this usage does in fact exist, though still without apparent documentation in the usual sources. See this new question on EL&U.

Well, even if you use itch as a transitive verb, as the Merriam-Webster allows, it means “to cause to itch” or “to vex, to irritate”. So, you don't itch an itch as you would scratch it: itch, in that sense, is not synonymous with scratch.