@An**
the reason it is mentioned that it doesn't give you any more time is that for most Westerners on a tourist visa, there is little benefit or point to getting a re-entry permit, as they will get a visa-exempt stamp for free coming back anyway (which can also be extended for 30 days).
You CAN get a re-entry permit on a tourist visa, or extension, but are you sure you actually need one? The main use case for them on tourist visas is for nationals of countries that are NOT eligible for visa-free entry, where their visa is their only means of getting into Thailand and they need to keep it active while visiting Angkor Wat or whatever.
There are some really marginal edge cases where it make make sense even for a Westerner, but make sure there is actually any point. I certainly don't see why you would want a re-entry on your extension, it only really makes sense if you would be leaving and re-entering in the first 30 days... but there can be edge cases where it makes sense, just make sure it actually is something you need to do, rather than just coming back and getting a free 30 day stamp.