This is just my opinion and I am NOT a tire guy (though I sometimes play one on the internet).
I would say, "no". Mostly because of the different tread footprint you will get at the same tire pressures. As I understand the differences between say C and D load range, the sidewall strength is much higher in the D rated tire and will result in a smaller tire footprint (tread in contact with the road).
How that will impact actual handling, I have no idea; but I do know that mixing bias and radials are prohibited and sidewall belts are part of that I am sure.
Again, a huge caveat; I would not mix them except in case of a greater emergency (like getting the rig home (or to a tire store) after a blow out).
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW