I have the feeling we could try, say, enforcing the laws we already have.

There are a whole host of ways you could encourage it without actually forbidding it, or as a prelude to it, which would probably be more politically acceptable. For instance you could progressively tax companies depending on the size of their profit or turnover. You could withdraw or reduce depositor protection from banks that are bigger than X.

You almost certainly have to come up with a measure that affects companies locally as many/most are based overseas. Global agreement on this isn't likely anytime soon so local regulation of some sort seems inevitable.

Actually, until the past several decades, big was bad according to antitrust law

Brad DeLong describes the situation as follows:

During the Great Depression, another principle was added to the mix. Congress decided the government should put its thumb on the scale on the side of relatively small producers: There was a public purpose to be served in outlawing practices that made it difficult for the small-scale producer to survive alongside oligopolistic giants, even if they were not the lowest-cost producers, even if the giants' practices were not necessarily unreasonable restraints.

Thus, antitrust became a tangled web of different laws pursuing contradictory purposes. For most of the past 50 years, lawyers, judges and analysts have gradually picked that web apart. The Chicago school of economists shifted from being enthusiastic advocates of aggressive antitrust enforcement to advocating a hands-off position. Future Judge Robert H. Bork suggested that antitrust law be revised to focus solely on consumer welfare.

Over the years, Bork's view gained strength. People scratched their heads as they watched the virtual repeal of antitrust statutes like the Robinson-Patman Act undertaken by those who in other areas (civil-rights law, say) exalted the original intent of legislatures and decried judge-made law. But it was not clear that small-scale producers deserved a special edge. A looser approach recognizing that close business links could be beneficial seemed likely to make us all better off.