Platylophus was found sister to
Lanius by Jønsson et al. 2008 [
pdf here] and by Aggerbeck et al. 2013 [
pdf here]; Jønsson et al. 2016 [
pdf], in a supermatrix analysis, recovered it sister to
Eurocephalus (and this group sister to
Lanius). But, as I noted in the thread referenced by Peter, this last inference is problematic, because the data set that was used included no gene that has been sequenced for both
Platylophus and
Eurocephalus (the data are on [
Dryad]; they used only ND2 for
Eurocephalus; GAPDH, MYO and ODC for
Platylophus).
Bird families of the world recognises a monotypic family Platylophidae, but I'm unclear that this name was ever made available. (I'd be interested if anyone knows a possible source.) And, of course, under this treatment, the monophyly of their Laniidae in uncertain.