You could just define the second to be a 1/100,000 of a day and go from there. Aside from screwing with literally everyones perception of time, it could work.
[0]: https://www.nasa.gov/topics/earth/features/japanquake/earth2...
But an even bigger issue is that the sidereal day (one 360° rotation of Earth as measured against distant stars) is not 24 hours but roughly four minutes less. And the length of the solar day also varies over the year due to the slight eccentricity of Earth’s orbit—days near perihelion are slightly longer than near aphelion. And then there are the higher-order effects caused by gravitational interaction with other planets...