Presumably pain works in some specific way (or some relatively narrow distribution of ways), so there probably is a maximum amount of pain that could be experienced in any circumstance. Real-life animals can and do die of shock, which seems like it might be some maximum 'pain' threshold being exceeded.
But suffering seems much more general than pain. Creating (e.g. simulating) a consciousness or mind and torturing it increases global suffering. Creating multiple minds and torturing them would increase suffering further.
What seems to be different about suffering (to at least some degree – real-life beings also seem to suffer sympathetic pain) is that additional suffering can be, in effect, created simply by informing other minds of suffering of which they were not previously aware. Some suffering is created by knowledge or belief, i.e. spread by information. (This post has a good perspective one can adopt to avoid being 'mugged' by this kind of information.)
The creation or simulation of minds is presumably bounded by physical constraints, thus there probably is some maximum amount of suffering possible.
Are there possible minds that can experience an infinite amount of pain or suffering? I think not. At a 'gears' level, it doesn't seem like pain or suffering could literally ever be infinite, even over an infinite span of time, tho I admit that seems true because it does seem true that, e.g. there's a finite amount of matter in the universe, and that minds cannot exist for an infinite amount of time (e.g. because of the eventual heat death of the universe).
But even assuming minds can exist for an infinite amount of time or that minds could be arbitrarily 'large', I'd expect the amount of pain or suffering that any one mind could experience to be finite. But, under those same assumptions (or similar ones), the total amount of pain or suffering experienced could be infinite.