It's probably a questionable assumption that screen will be installed on the jump host. Those machines usually have pretty minimal systems.

Sometimes multiple xterms are easier than using screen with multiple buffers.

In that case you could connect to the same screen session in all of the xterms (see screen -x), but have them display different buffers.

How does that help? You'd either still have to connect to the remote server multiple times (if screen runs remotely), or you're going to have to connect multiple times from inside screen (if screen runs locally)...