There are several guidelines out there as many above have attested to. You most definitely should go at least 2 footing widths if on spread footings and perhaps deeper if on piles (subject to what you hit - i.e., rock) as the zone of influence of a pile group is greater than the "size" of the pile. But, I trust that you are working for a reputable soils firm - if you are, then you should have senior engineers who can explain this - much is really based on experience and judgment and of course on the nature of soils encountered. I agree, I DO NOT WANT ASTM TO SPECIFY SUCH. They have damaged geotechical engineering enough in my view.
As for the original post, it appears that you have dug a big pit - even though you found "poor" soils below the founding level, to me it appears that you have removed a lot more load in your excavation than the weight of the structure you are putting in - this, then, if you use a rigid raft and walls becomes a bouyancy raft or compensated foundation - if the loads are such that the load removed is more than that applied, you shouldn't get any additional settlement. Foundations on such foundations have been founded within poor soils successfully.
Cheers