I have an Iphone 5s from AT&T. Is it possible to switch over to Verizon with the same phone?

I have an Iphone 5s from AT&T. Is it possible to switch over to Verizon with the same phone?

Would be up to if Verizon would get the phone on the network.

I don't think so. AT&T is a GSM carrier while Verizon is a CDMA carrier. They require different wireless bands and only the model you choose will have the right ones for that company.