Robert:
I don’t know of any reason why you wouldn’t normally be able to use both continuous and spread footings (ftgs.) on the same bldg. It’s for you to determine when you need an engineer, but it’s also your risk if you do it wrong and/or don’t know what you’re doing. You said ‘2'x2'x required depth for individual ftgs. for masonry piers’; what is the required depth, and how do you determine that?
You have to understand the soil conditions, be able to identify various soil types and their bearing capacities, and some of their idiosyncrasies. That is; do they heave if frozen, swell or shrink due to moisture changes, consolidate under ftg. pressure, etc. You should have some means of judging the soil compaction, know when you need to do mechanical compaction, know when you have to dig out a soft spot and fill and compact it in small enough lifts to provide proper compaction. And, you want to size your ftgs. so the soil pressure and thus the potential deflection (settlement) is about the same on all of them. GeoTech Engineering is serious business, too often ignored in light construction, but this is at your own risk. My Structural Notes say that you should hand excavate the last few inches to bot. of ftg. elev. so the ftgs. are placed on undisturbed soil, virgin soil or soil which has been properly compacted back up to b.f.e. I do not want you placing ftgs. on 3 or 4" deep tooth marks from a backhoe, and the like.
You have to have some understanding of how the two different ftgs. work. The continuous ftg. can basically be a little wider than the wall thick. + 2(ftg. depth) without any need for reinforcing (reinfg.) across the ftg. to account for ftg. bending under load, and then you only put in a few longitudinal bars in the bottom with 3" of cover above the soil. For example, a 12" wall on a 12" deep ftg. could be 3' wide without short cross reinfg. in most cases. A poured conc. wall is stronger than a grouted masonry wall, is stronger than a hollow mas. wall, is stronger than a pressure treated wood foudn. wall, generally in that order. And, as these walls get higher, they act as a deep beam, in the above descending order of strength for conc. or mas., not for wood though, which will help the ftg. span small soft spots, and that’s a good thing.
The spread ftg. (you said individual ftg.) might be placed on a soft spot, which can come back to haunt you, as the ftg. can settle uniformly or rotate during settlement. The spread ftg. can be depth + pier size + depth, in size, in each direction without much concern about reinfg. in either direct, but I’d still put a few bar in the bot., 3" cover again. If the ftg. gets larger in dimension than above you have two concerns, you need to start designing reinfg. to prevent bending failure and you must guard against a punching shear failure. Imagine an 8x8 post punching (pushing) through the ftg. under less load than might cause a 12x16 grout filled conc. blk. pier to fail.
Once you know the ftg. size and the allowable soil pressure you can calc. how much load that ftg. will carry, and that’s usually expressing as lbs./ft. for a continuous ftg. and in lbs. for a spread ftg. and pier. You determine the load on either type of ftg. by adding up all the bldg. loads which are applied to that ftg., and this is a function of your bldg. framing system and layout.