Can I pair more than one iPhone to my Apple Watch?

No. At this time, each Apple Watch can only be paired to a single iPhone. It's not possible to pair multiple iPhones to one Apple Watch.

The Apple Watch communicates via Bluetooth to specific iPhone apps, and requires a unique connection with that iPhone to work properly and exchange relevant data. Switching to a different iPhone on the Apple Watch would require syncing data and setting up the new Apple Watch every time.