First of all, get advice from a qualified legal professional.
My (layman's) reading of 2-clause BSD license is that that would be permitted, provided that you retain the original copyright notices, and include the required disclaimer notice.
Bear in mind that when you fork someone elses codebase, their copyright is not "extinguished". They will hold, and will continue to hold partial copyright on your codebase ... to the extent that your codebase includes parts of their code. This is why you >>should<< talk to a lawyer.
I would also recommend talking to the original copyright holders first. They may not care, but they might have views on whether forking is a good idea. Generally speaking, forking a project leads to various inefficiencies ... to the detriment of both projects, and the people who use the software.