Will there be breakups for some corporations becoming too big or too powerful?
No. We live in a world where transnational corporation exists. Apple has a larger GDP of some nations. Because corporation growth extends past the laws of most countries, we can’t pass laws which limit their growth. In fact, a major failing of the ICC and UNSC is they don’t care much about this area, because they consider it territory of the Wold Bank. The problem being one is about applying the Rule of Law and one is about facilitating the world markets.
What we can do is observe our rules regarding monopolisation and cartel-conduct and advocate for good, transparent, accountable corporate governance. Monopolisation you no doubt understand, but Cartel Conduct is when two corporations get together and more or less act together without competition, to the detriment of the consumer. Most western jurisdictions have good laws and bodies which facilitate the prevention of this, and for the most part we do a good job.
On Monopolisation, when Disney and Fox merged, there was a legal battle over whether it was justiciable because the question was whether the dominant market share would approach market control and promote anti-competitive behaviour. As you know, this didnt happen, and it was won on the data (as opposed to the law). This was probably the correct ruling, to be frank, because despite common perception, the economics does not indicate this merger has created (or more correctly will create) market control in any of the markets that Disney and Fox operate in. The important thing here is to understand what market control means in a legal sense, as opposed to common parlance, and that is to create a situation where competitors have no economic option but to vertically integrate with the dominant market force.
More controversial is the merger between AT & T and Time Warner, which the data DOES NOT support, was appealed and still approved.
With this said there HAVE been both horizontal and vertical mergers which have been knocked down, and to my memory they almost exclusively relate to Banks – so that may tell you something.