You can bet that if the board of directors could show that unscrambling the omelet would result in greater shareholder value produced, it would suddenly be really easy to do...
On a technical level it would still be a nightmare. But yes it would actually get done.
Happened with Dow-Dupont! A three-way split, even (from a two-way merger). Took roughly two years and was the shareholders' plan from the start. By most accounts it went very smoothly.
[1] https://www.investors.dupont.com/news-and-media/press-releas...
[2] http://www.dow-dupont.com/