[MPlus] Using the Alignment Method with non-invariant factors

I am attempting to use the Alignment within CFA method from Marsh et al. (2017) on 2015 PISA. However, six out of nine factors have more than 25% non-invariance What can be done to a dataset that is found to be mostly non-invariant using the alignment method? Does this mean than the 6 factors can not be compared across countries? Or is there other procedures I can use?