Can multiple websites be synchronized under the same CRM installation
It is possible to have a single civicrm wired to several CMS instances.
There is some documentation here
https://docs.civicrm.org/sysadmin/en/latest/install/multi-site/
There are hurdles to get over, for example, how to synch users across the various CMS
There are other approaches to pull in data from other sites without wiring CiviCRM in to it including

Remote Forms

Profiles using HTML snippets

using the RestAPI


Some good answers here
Perhaps best if you want more input on this Q+A to add more info to your Question detailing a bit more including how you see logged in users functioning across the sites