Stability shouldn't be an issue as there's not really anything prone to buckling in Ste system. I think that your issues will be just ordinary bending and deflection based on what remains of the grating. If you post a scaled plan sketch showing the cutouts, we'll be able to offer more detailed advice.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
If this is bar grating, I used to design strongbacks (sections of angle) to "header" grating openings and transfer the loads of the cut bearing bars to adjacent uncut bearing bars. Last resort is to install trimmers to carry the headers.
Several decades back I was working on some cranes that unloaded containers from ships at the Conley terminal in Boston, MA. There were outdoor walkways all around the ~100 foot level. A section of the open mesh expanded metal deck had been installed oriented the "wrong" direction. I may never forget The first time I stepped onto that section of the walk, and it sagged noticeably beneath my feet.