The 32x32 magic is not only an even multiple of 4, but 4x8 (or 8x4) and that gives many possibilities to construct a 32x32 magic square.
Methodes to construct the 16x16 magic square are:
Symmetric transformation (Liki) and basic key method (ultra magic) leads to ultra magic 32x32 squares, which are panmagic, symmetric, 2x2 compact and each 1/4 row/column gives 1/4 of the magic sum.
The Medjig 32x32 magic square, composite 32x32 (1) and (2) , the concentric 32x32 magic square and bimagic 32x32 are 'specials'.
With the remaining methods you kan construct most perfect (= Franklin pan)magic 32x32 squares.