This is perfectly doable, yes, even if it would mean a lot of work and legal research. After all, LibreOffice is a fork of OpenOffice, which was based upon the German StarOffice.
StarOffice was proprietary software, but it had been ported to GNU/Linux and it was free of charge for personal use. Sun Microsystems then bought StarOffice and released a modified and open-sourced version of it as OpenOffice.
Sun Microsystems was then acquired by Oracle, who immediately nuked their sponsorship of the community-developed OpenSolaris and forbade anyone to use the name Solaris ever again, and there were concerns that Oracle would soon come to do the same with OpenOffice.  So OpenOffice was forked into LibreOffice, and just to spite the LibreOffice developers, Oracle then donated OpenOffice itself to the Apache Foundation.
But it all began with StarOffice, back in the 1990s. I've even used StarOffice myself in my very first GNU/Linux distribution, the commercial Linux-Mandrake 6.0 PowerPack.
- There were similar concerns with regard to MySQL, which is why the original MySQL developer forked the code into what is now called MariaDB.