Pouchdb/Couchdb can be used to build a self hosted alternative. With pouchdb you get replication to any couchdb like backend, offline storage in the browser (which neither parse nor firebase offer yet), and it runs on a number of platforms - browser, mobile, standalone server with several backends including levelup/down and SQLite. There are a number of node modules that will allow you to build a PaaS like self hosted backend (if thats even a thing), one such module is superlogin,
https://www.npmjs.com/package/superlogin. It offers an angular client, I'm also building a vanilla js version for it that can be used without angular -
https://github.com/dryajov/superlogin-client. That said, Parse server has been open sourced, and it might just suit your needs.