There is no explicit, enumerated Constitutional power granted to Congress or ANY branch of the federal govt to break up free enterprises. Indeed, the Congress didn't seek to break up US offices of the East India Company. The Sherman Antitrust Act draws its legal underpinning from the Commerce Clause, perhaps the most abused element of the Constitution. To give sanction to a federal break up "monopolies" via the Sherman Antitrust Act, i.e. the Commerce Clause, is to give sanction to every other abuse of the Commerce Clause from the New Deal up to the Lopez decision.
In 1995 many people (including Robert Bork...while on Netscape's payroll) argued that Microsoft should be broken up. It wasn't. In response, several firms had to rely on innovation and the free market. The result? I can post to FR while commuting to work, while Microsoft isn't the Master of the Universe anymore.
I don't like what FB et al are doing. But the same means by which many want to grant the government the power to regulate a few servers and wires that NOBODY IS FORCED TO USE is the same means by which guns can be regulated out of existence, dissent can be quashed, and state socialism/governmental choosing of winners and losers can be enacted.
Usually people weidling phrases like "monopoly" and "anti-trust" - which are found NOWHERE IN THE CONSTITUTION with regard to congressional power - aren't free marketers. Now, right is left...Indeed, when conservatives start talking like philosophical cousins of Al Franken then we have a problem.
Does anyone really think the Deep Staters and this colossus giving us the IRS, Obamacare, the EPA, DACA, the IRS, and the Kelo ruling etc would really make the FB and Google et al situation better? As I wrote elsewhere, empowering this govt to go after these private actors could result in some twisted result where all citizens are then REQUIRED to have a FB and Google account or else you'll have to pay a fee/tax. It can't happen here? Look at all the legal rulings blocking Trump's efforts on immigration. Look at Roberts' Obamacare opinion.
Asking today's Deep State-backed Leviathan to save us from FB and Google is like asking Hillary to protect our embassy in Benghazi.
We little people have to solve this with private action. I'm sorry...I'll chose the Founders' intent and freedom over state socialism any day.