For something to experience pain, some information needs to exist (e.g. in the mind of the sufferer, informing them that they are experiencing pain). There are known information limits, e.g. https://en.wikipedia.org/wiki/Bekenstein_bound or https://en.wikipedia.org/wiki/Landauer%27s_principle

These limits are related to entropy, space, energy, etc., so if you further assume the universe is finite (or perhaps equivalently, that the malicious agent can only access a finite portion of the universe due to e.g. speed-of-light limits), then there is an upon bound of information possible, which implies an upper bound of pain possible.

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.

One possibility is "a lot", in that humans seem to interpret pain on a logarithmic scale such that 2/10 pain is 10x worse than 1/10 pain, etc.. However, there is likely some physiological limit to how much sensor data the human brain can process as pain and still register it as pain and suffer from it. This leaves out the possibility of modifying humans in ways that would allow them to experience greater pain.

Note that I also think this question is exactly symmetrical to asking "what's the maximum level of pleasure", and so likely the answer to one is the answer to the other.

Presumably, you are asking because you want to calculate the worst-case disutility of the universe, in order to decide whether making sure that it doesn't come about is more important than pretty much anything else.

I would say that this question cannot be properly answered through physical examination, because the meaning of such human words as suffering becomes too fuzzy in edge cases.

The proper approach to deciding on actions in the face of uncertainty of the utility function is utility aggregation. The only way I've found to not run into Pascal's Wager problems, and the way that humans seem to naturally use, is to normalize each utility function before combining them.

So let's say that we are 50/50 uncertain whether there is no state of existence worse than nonexistence, or we should cast aside all other concerns to avert hell. Then after normalization and combination, the exact details will depend on what method of aggregation we use (which should depend on the method we use to turn utility functions into decisions), but as far as I can see the utility function would come out to one that tells us to exert quite an effort to avert hell, but still care about other concerns.

When pain is unbearable it destroys us; when it does not it is bearable. Marcus Aurelius

The goal of increasing the suffering contradicts the need to preserve an individual, who is experience the pain as the same person, which may be a natural limitation for intensity.