migrating to CI4 mantaining the old site

HI!
This is the situation:
i got a site with my company php framework... we are trying to upgrade the tecnology by using Codeigniter 4 Framework.
Is there a way to mantain both frameworks running like one site and migrate the diferents apps gradually making a switch between boths urls?

im guessing that there will no problem with the urls cause CI4 is using public to execute the app, but... what about the sessions? can the two sites share the same sessions?
Thks in advance!