I think your problem is that your patch element is becoming multimoded at the higher frequencies. Multimoded is not necessarily a problem if you can prevent the power at the higher frequencies from exciting the higher order modes. Can you make your patch more symmetric including the feed? Can you reshape the patch to push the second order mode to a higher frequency? You could inductively couple a smaller patch to some outer patches. At lower frequencies this will behave as one large patch while at higher frequencies the outer regions would be choked off. This is a similar concept to well-known taps in thin wire dipole antennas.
Just some thoughts.
Adding to Raymond ,you can get transmission nulls at the intended frequencies by introducing suitable defective ground structures DGS under the feed line. I think it is an effective way to stop the input from entering the antenna at the specific nulls.
wish you succes
As Abdelhalim Zekry said you may create regular constant disorders in the patch so higher modes can be reduced.
I mean disorder means at every constant distance make a point punch on patch.
You have to modify the shape of the patch. Try a non-rectangular patch, or introduce some irregularity in the geometry.
Are you using patch array or dimensions are greater than half wavelength? The possibility of null is due to multipoint radiation and coherent signal added out of phase. To remove null, structural part to be analysed and in case of multi point radiation, phase part to be taken care
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