Large mat foundations are usually modeled using plate elements and the boundary conditions at soil – foundation/structure interface is idealized using winkler springs assigned with sub-grade modulus of soil (using plate mat with compression only springs in STAADPro to establish and take into account the loss of contact, if any). Needless to say, such an analysis is non-linear in nature and time consuming as it involves several iterations spreading over the entire set of load combinations in order to obtain convergence of results in each case.
For service level load combinations, foundation sizing is carried out based on the maximum bearing pressure, stability ratios (overturning and sliding) & estimating / limiting the contact area thus obtained.
Usually, the above sized foundation is then re-analyzed using strength level load combinations to obtain bending moments & shear forces at the sections of interest, in order to design the concrete thickness and reinforcement required.
Now, the point of discussion here is, should such foundations be re-analyzed in STAADPro (or any other analysis software) using the strength level load combinations in order to obtain the design forces?
OR
Should the internal forces obtained using service level load combinations above be simply magnified with strength level load factors to arrive at the strength level design forces?
That's a good question and one that also applies to Ram Concept or Ram Foundation. We usually recommend an analysis of the factored load combinations to yield the strength level concrete demands. It is possible that these factored load combinations could result in an instability while the service combos are all stable, but those cases tend to be the ones where users are "pushing the envelope" anyway, so making the footing larger to stabilize factored load combinations is reasonable.
I know a few users who prefer to amplify the service forces as you suggest, and that seems fine so long as the load factor is conservative.