Can I send a fleet to more than one destination?

Yes, it is called Waypoints.

in the Move Fleet page, you can inform more than one coordinate. Or select more than one option in the Coords List with your bases, fleets, bookmarks and occupations.

After reaching the first destination, your fleet will wait the auto-launch that happen every 5 minutes server time (0m, 5m, 10m, ...)

You can use it to take the advantage of a base with Jumpgate, or more than one base, to finally reach your intended destiny.