I did add a second muffler to my Winco 5KW generator, engine is a B&S Vanguard 11HP. It did quiet it down but not as much as I expected, the mechanical noise became dominant. Next step was to built an enclosure with fans. I did not do it because the generator will not be portable and worried about having the generator and gas tank inside an enclosure (fume and spark?).
I also have a Honda EU6500is. It use a GX390 engine. The muffler is extremely quiet. It is mounted diagonally behind the flywheel/alternator and I doubt it can be retrofitted to other generator because of the compact and custom design. The multi-phase alternator is the one that feed the inverter, it is more compact than a conventional generator. This generator is very quiet, I cannot hear it in the house when is running on the back patio. It is also powerful, it can run the first floor central AC in low stage. The unit is a two stage 3 tons (36K BTU) high efficiency (SEER 20).