Yes there are(some places that won't offer the extra servicies). I have read news that once several guys offered extra money for "extra service" but were rejected by the massage girls. Those guys got angry and hit the girls. Later the men were sued and sentenced and had to compensate for the injury. 

No. There are many that would be deeply offended if you even asked.

The pink light places will do so. The others, be careful before you ask.

Related question: are legitimate massage shops open at midnight? I can't help but feel depressed everytime I walk by that one place. I find myself contemplating slave labor and the ethics of human trafficking whenever I go for a late night stroll.

To answer your question, there are lots, if not the majority of massage places that won't provide additional services.

Of course, as was stated by someone else, if they are open very late, they probably aren't one of the legit establishments.

Mr NiceBrice:

If I may offer a suggestion, before you go to a massage parlor, and so you have no worries, do stop at a pharmacy and buy a pair of surgical gloves, and ask the person giving you the massage to wear them before touching you, and end of worries.

Now, if you have to ask for "extra services", most probably the parlor does not provide therm, because those that do and are willing to, as soon as they get you "away from the crowd", will make a sales pitch to you.  So, if they do not, it is because either they dislike you, or do not offer anything else than a massage.

Now, if you really want one hell of a good massage, seek at the city where you reside a parlor using blind persons as workers.  Do not know why, but they do give a good massage.  I do get one maybe on a once per week basis,  and cheap too.