Overwhelming means more than can be handled. Underwhelming often means less than can be handled or expected. Is there a word to mean exactly the upper limit of what one can handle without becoming overwhelming? Something akin to of upper-but-not-overwhelming.
Actually "whelm" already means "to turn upside down". Overwhelm is an intensification used figuratively and means something similar to "completely turn someone's military forces, mind, or whatever, upside down".
Underwhelm does not mean that something gets turned in the other direction, but that it does not get turned at all. Etymologically underwhelm was not derived from whelm (under + whelm), but from overwhelm (under + overwhelm). Underwhelm is a quite recent neologism (Merriam-Webster: 1948; OED: 1956) from what I call "adolescent coolspeak" (the OED more scientifically calls this "jocular"). You can understand it to be the ironical neutralization of overwhelm, the undoing of the turning. Underwhelm therefore does not, as you claim, mean "less than can be handled", but rather "can be handled quite well" or, as the dictionaries put it, "fail to impress" (the audience), i.e. "leave (the mind) unturned".
Between "turn" and "not turn" there is no third option. Either you impress your audience, or you bore them.
In the context where underwhelm is used, i.e. in the context of movie reviews and audience entertainment, overwhelm is what the audience seeks and what the producers strive for: an exciting media experience, while underwhelm is the failure to entertain and must be avoided. Overwhelm in this context is the word that you look for and means the exact right amount of fun.
In other contexts, where underwhelm cannot be used, and where overwhelm has a negative meaning of "too much", the alternative has a positive connotation: your forces where not overwhelmed, you are not overwhelmed with sorrow, etc. In this context, what you look for is the calm (unaffected) and competent state.
(Over)whelm is a duality. In both cases, the too-much-is-fun and the too-much-is-bad situation, there is logically only one alternative to overwhelm, and that is "not too much", which outside of media reviews, where you can use underwhelm, does not really have one specific word to describe it, because the perfect state that is disrupted by overwhelming varies.
If you want to get away from the dichotomy of what Drew in his comment calls "to whelm or not to whelm", and name the perfect stimulation, between overstimulation and understimulation, Csíkszentmihályi (1975) calls this balance between skill and challenge "flow". And flow, in the theory of motivation, is the result of a situation that is neither overwhelming (too difficult) nor underwhelming (boring), but motivating:
To finally answer your question, "the upper limit of what one can handle without becoming overwhelming" is
Depending on the textual context, other words - like pleasant, satisfying, inspiring, and so on - might fit as well or better. For example, the just-right middle between overstimulating and understimulating might be described, quite simply, as stimulating. But pleasant, satisfying, inspring, and stimulating, as well as all other possible words, don't necessarily mean that the input you get has the perfect level of stimulation. Less than the right amount can be pleasant and satisfying, more than the right amount is still stimulating – because overstimulation is still stimulating, isn't it?
So why motivating?
Let's try to answer the question by turning it around. Instead of searching for a word that names the right level of stimulation, we look at what the right level of stimulation causes, and that is: full capacity (or any synonym thereof). Assuming that your senses and emotions have a maximum (which is implied by "the right level"), that maximum is "full capacity". Now that we know what is caused by the right level of stimulation, let's try and find out what causes what is caused by the right level of stimulation.
If that argument was confusing, maybe a schematic representation helps. Stimulation can be seen as a continuum from no stimulation to too much stimulation, with the perfect level somewhere in the middle:
no stimulation -> too little stimulation -> right amount of stimulation -> too much stimulation
Now, let us call "the right amoung of stimulation" RAoS, so we don't have to type that phrase every time. The sensory organs or emotions of a person receiving the RAoS, will be at full capacity:
right amount of stimulation (RAoS) => full capacity
Now, if we ask: What causes full capacity?, the answer would be: RAoS. Right?
x => full capacity x = right amount of stimulation
But there is another answer to that question.
For more than a hundred years, industrial and organizational psychology has tried to find an answer to the question what motivates workers to perform at full capacity. For more than a hundred years, pedagogical psychology has tried to find an answer to the question what motivates students to learn at full capacity. Do you already see a pattern? (Yes: "motivates".) The answer that has been found to all these questions is: the right level of stimulation. Now, that was what we had in the beginning, wasn't it? No, because we forgot a step. The right amount of stimulation causes, not full capacity, but motivation, and motivation causes full capacity:
RAoS => motivation => full capacity
Now, if RAoS causes motivation, then what is it? Simple: motivating. Because what is motivating causes motivation. So, the right level of stimulation is motivating:
RAoS => motivation motivating => motivation RAoS = motivating
To return to the beginning of this argument, of course pleasant, inspiring and stimulating things also cause motivation, but with the general question that we are given and in the absence of a concrete case of application, motivating is the most general, all-purpose answer.