Absolutely....I have done it by mail and by online.
The best way I have found to do this is as follows:
1. Fill out the I-129 for the TN extension or new employment - or whatever it is you are doing online and submit.
2. Once the I-129 is submitted, it will tell you where to send all of your required evidence (diploma, offer letter - he needs a new offer letter even if it's for a continuation of present employment).
3. Fill out I-539 (you cannot do this online) for the TD (s). Gather the info for this - don't forget to show a copy of your marriage certificate - passports and/or driver's licenses are not enough.
4. Once all of this is submitted, you are good to continue staying for 240 days until your new I-94's are sent to you.
5. If you need your I-94's ASAP (like for employment with a new company), then, yes you can pay the extra $ 1,000 for premium processing. If you are not traveling out of the country any time soon or it's just an extension of present employment, then why pay the extra money. If you do leave and then come back, you can get a new TN at the border when you return.
Remember - the new I-129 needs to be submitted before the present TN expires. As long as they receive it by the expiration date, you will be okay.
In addition to all of this, look at the posting yesterday and today by BrianG about his fiancee getting refused at the border for her TN.