Yes! There are at least two ways to do this. First, you can define a 1D unit cell composed of your multiple layers. You will then Fourier transform this into a set of planar gratings, spatially vary each of those, and then add them up to get the lattice you want. Second, you can spatially vary a single planar grating and use two threshold values to create three values of epsilon.
If you are a bit unsure about what I am saying, let me point you to a short course on generating spatially-variant lattices that may help. Here is the link:
I agree with Sir R. Rumpf. epsilon value affects your lattice structure, but it does not mean that while forming a lattice, one can not introduce one more epsilon. As Sir said above, by defining the one dimensional unit cell and taking fourier transform is the best way to add in threshold function and one can control other variations while forming the lattice. Even, sometimes, this is being used for PBG structures for single mode operation.