Comment by bluGill

In theory yes. In practice a web engine is so complex you need a large team. Your fork may start out good, but quickly it will become so far behind everyone else that it isn't usable as a browser for the latest sites. Plus you won't hear about many security issues/fixes until you are exploited.

Unless you can find a large team willing to maintain your system a fork is something that is not realistically possible. As volunteers I doubt you can get enough help, but if you are rich you can hire plenty of developers who would love to help.