Can you set up a wordpress (multi-site) network to work across multiple hosting accounts?

A multi-site network only has one set of files:

  • There is only one WordPress installation that is shared among the various sites.
  • There is only one database shared among the various sites.

The database and WordPress files don’t need to be on the same physical machine, but they need to have access to one another.

The WordPress files must be on one machine (hosting account).

The database can be spread across multiple database servers using sharding (See the SharDB plugin for an example).

If you want your various sites on different hosts, then you really need to have different WordPress installations. Read: Not multi-site.

There is a service available for managing multiple, standalone sites called WP Remote. You might want to look into that …