@Anthony *****
yes, that is correct. Although it is always recommended to double check with the office you will use as it seems someone else stated that the office they went to would not allow them to do both. Even if it is the same office that told me, as supervisors and rules change.
In Chiang Mai a few years back I let my 12 month extension expire on purpose so I could start over in order to change the timing of my 12 month extensions. I entered on a visa exempt and only wanted to do the 60 day extension to make it fall on a more desired month. The immigration officer said I should do the 30 day extension first, then the 60 day extension because if I did it the way I wanted I would not be eligible for the 30 day extension. They understood why I didnt want to do that once I explained it to them.