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I'm sure it's not the only solution, however you can...
(1) introduce 'cuts' onto your radiating patch
(2) introduce another 'image patch' fed with 180-degrees-out-of-phase to the main signal, like a dipole!
A -40 db SLL is possible but you are getting into an area where the design will be very fussy. Generally to get to that kind of level the element patterns need to have excellent F/B ratios and you have to be very careful with feed line leakage.
You are looking at need heavy amplitude tapering to get close. Measurement of the array will not be easy either.
As a general rule when the gain of the antenna and the SLL get close to eachother things get difficult. You mention what may be a large array and thus high gain so it is possible but certainly not easy.
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