Countermeasures to prevent integral cryptanalysis against 4-rounds AES
This question may be theoretically interesting. 

However, it looks to me strongly likely that the nice diffusion properties of AES using operations of order $4$ ShiftRows) and matrix ($4\times 4$) multiplication on vectors of dimension $4$ (MixColumns) are the reason for the existence of these attacks and changing these properties may well require more rounds for security.

The requirement that these operations be one-to-one, in the absence of a feistel structure, means that the SPN structure may also need to be dumped in order to avoid 4 round integral cryptanalysis.