Hello!
I have extended by non-im type o (based on Thai dependent's) for the last five years.
One of these extensions has been a 60 day extension.
The others have been year extensions.
Now, I understand we are only allowed to use the 60 day extension once on the same visa.
But, I have recently obtained a new passport and have had the visa extension transferred.
Does that mean that I can apply for another 60 day extension?
I seem to recall an immigration officer at Chang Wattana, saying that is the case.
Would like to hear from anybody who has tried this before making the trip.
Many thanks! 
 

Getting a new passport will not erase the record of previous extensions in immigration's database. When they transferred your stamps to the new passport  they linked the your history from the old one to the new one.

You could try it but I suspect they will notice the previous 60 day extension.