The move, which sees Franks depart, comes three years after the agency, formerly Borkowski PR, relaunched following the departure of Mark Borkowski.
The agency retains clients including Häagen-Dazs, Pioneer, Zumba Fitness and Dogs Trust.
Greenwood, who took over the MD role from Franks last summer, said: "My vision for See.Saw is to become a serious player in the boutique agency sector and shake up the way we operate.
"We’re a small nucleus of highly experienced, passionate people, working with a bigger pool of like-minded specialists and freelancers on bigger brand collaborations. We have already formed an exclusive partnership with Alchemy Digital, working together on digital strategy across our client base."
Larry Franks, owner of Beige, added: "This is all about timing; perfect timing for the agency, for Megan and for myself.
"After 20 years in the industry, this could be seen as a semi-retirement, but the truth is that I no longer want the full-time commitment that owning an agency brings. It's some time I need to pursue other business interests.
"Megan and I have worked together for almost 15 years, since 1999 at The Wright Partnership, then at Borkowski for eight years before Beige, so this feels like a very natural progression for us."