Voevodsky wrote on his papaer "Open Problems in the Motivic Stable Homotopy Theory, I" that

Three other groups of conjectures in motivic homotopy theory, not included in to this paper, seem to be slowly crystallizing. One group describes the behavior of slice filtration with respect to the functors $f^*$ ; $f_*$ ; $f^!$; $f_!$ for morphisms of different types. (page 5, page 3 on the pdf file)

However, appart from Pelaez's paper studying its behaviour with respect to $f^*$, I have been unable to find any reference of these conjectures.

My question is: have these conjectures describing the functoriality of the slice filtration with respect to these functors been written anywhere?