Hmm. I think my TIAA plan is not truly a 401K plan, though I am not sure what the distinction is. Perhaps that is why I am (apparently) allowed to contribute a full $23,000 to that plan as well as $23,000 to the 403b plan. In any case, I will double check with HR, TIAA, and my tax guy.
I am not even close to contributing $46,000--in fact, just putting aside $23,000 will be a stretch, so I am not very worried about it. But it would be nice to know.