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:
For the 32x32 magic square I do not show how to composite the 32x32 magic square (see 12x12, 16x16 or 20x20 magic square) or how to use symmetric transformation (see 12x12, 16x16 or 20x20 magic square).
Basic key method (ultra magic) leads to an ultra magic 32x32 square, which is panmagic, symmetric, 2x2 compact and each 1/4 row/column/diagonal gives 1/4 of the magic sum.
The concentric 32x32 magic square is a 'special'.
With the remaining methods you kan construct most perfect (= Franklin pan)magic 32x32 squares.
I present only one option of the basic pattern method, which leads to a most perfect (Franklin pan)magic 32x32 magic square with the extra tight Willem Barink structure; see more options on the webpages of the 8x8 magic square.
See below the downloads of Sudoku method (1) and analysis of a bimagic 32x32 square.