I believe you can do this with Mastodon, you can turn off all the federation features and have an individual twitter-like social network you can invite your fri

I believe you can do this with Mastodon, you can turn off all the federation features and have an individual twitter-like social network you can invite your friends to join. More commonly people are using groupchats on WhatsApp, Discord, or Slack for this... it's easier than maintaining it yourself (but there are also plenty of self-host options for chat networks too).