The short answer is "no."

There is no API to write to request bodies, only to read them. Previous to the move to the webextensions API (FF 57), it was possible. For example, there was an add-on called TamperData that was exceedingly popular. Since then, there have been other add-ons that have called themselves TamperData, but do not have the same capability.

The slightly longer answer is "maybe." It depends on what you want to do.

If you want to alter form submission in a POST request, you can intercept the submit event, alter the form, then allow the action to continue. (See Is there a way to modify the POST data in an extension now? for some discussion.)

If you want to alter HttpRequest bodies in general, you'd have to create a separate proxy to intercept them and alter them. You can't get an extension to do that.