I've searched the ideas repository before composing this request. There are a few ideas that partially overlap with mine, but I think my proposal is somewhat different from what's already been suggested.
I'd like Firefox Private Windows to provide an option to prevent websites from correlating separate private sessions as the same computer after my IP address changes. I know about Enhanced Tracking Protection and Total Cookie Protection, and I know Firefox prides itself for offering strong fingerprinting defenses. However, some of these approaches are not always effective, and are a little too heavy-handed anyway, particularly when applied wholesale to any site we visit. I would like a blacklist of domains that require extra anonymization - more so if they're opened in a private tab.
Using Brave or Tor Browser seems excessive, and especially the Tor Browser has a number of extra difficulties (try using Gmail with that!). I would like more user-controlled isolation of stable identifiers across Private Windows, possibly with an explicit compatibility warning when necessary.
Thanks for considering!