Operators cannot change thrust ratings, they can only change thrust limits. If you want higher thrust on your aircraft than the max thrust rating, you have to look at the aircraft type certificate, see if it was certified with an engine or engine mechanical configuration with a higher thrust rating, and if so, swap the engines or convert the engine to a new model configuration. If there is no engine or configuration listed in the TC with a higher thrust rating, then you have to pursue an expensive STC.
I suspect you are confusing thrust ratings (which are design limits from the manufacturer) with thrust limits, which are programmed in the FADEC. Two different things. A turbine engine may be rated for a certain thrust, but be limited to a lower MTO because of the aircraft in which it is installed. The former is fixed and documented on the engine data plate (along with the current configuration of the engine), the latter is programmed into the FADEC.
Turbine engines such as those used on the B737-800 have only two approved thrust ratings, the MTO (max takeoff thrust) and MCT (max continuous thrust). Everything else from there to idle are just manufacturer recommendations. The engines on the -800 are CFM56-7B engines rated at between approximately 18,500 and 34,000 pounds thrust within 49 different model numbers, as listed in the TCDS (Type Certificate Data Sheet). If an operator wants their engines to last, and minimize repair maintenance costs, they will do things like not push the engines to MTO when it is not needed, and less thrust will do.
When anyone adjusts thrust in the FMS for a particular situation, for example, what they are doing is NOT changing thrust rating. What they are doing is changing thrust limits, which the FMS them communicates to FADEC so it knows how to respond to pilot inputs in the throttle quadrant.
For those of you can deal with the FAA's technospeak, AC 33.7-1 goes through the process that an aviation turbine engine manufacturer must follow to obtain type certification, and explains the difference between thrust ratings and operating limitations. In essence, this confirms what I have already stated -- operators cannot change thrust ratings because that would require a new certification process for the engine, with all that that entails. Only limits can be changed and then again strictly within the performance envelope specified in the type certificate.