Units of Measurement
The length of the second, when combined with the mass of the kilogram and the length of the metre, gives us the size of other fundamental units like the ohm, the ampere, the watt, and the joule. So we can't change the length of the standard second.
But it certainly is possible to have civil time run on non-standard seconds, as was the case before 1972. Atomic Time is based on Ephemeris Time, and we could continue to have that as well.