Specifically, I'm talking about ear plugs or something in addition to headsets
Yes ! That's EXACTLY what you should be looking for ! There are lots of different types, sizes and makes available out there. Mostly just very simple and soft foam, which slip comfortably into the external auditory meatus ( ie your ear-hole ! ) as and when required. A standard headset can be worn over the ears exactly as normal.
Do NOT expect hearing protection to render you deaf ! Good hearing protection leaves you still able to hear normal things (including warnings of danger, etc), but just simply attenuates the most damaging peaks of excessive noise !