I'm reasonably confident this is not how it works.
First off, you need to establish what you're trying to do before making any roll. Our example Exalt wants to learn where the young mistress is. This can't be a Read Intentions action, because those can only reveal motives, Virtues or Intimacies. This means we're trying to Persuade the target to take the action we want them to take.
We mostly just glower and try to look scary, so we aren't pulling on a specific Intimacy to get our goal; however, this also means no bonus for us. Let's say our target has some Integrity, but not too much, so their base Resolve is 3, plus they also have a Major Intimacy of Loyalty to the family they're serving. This means we start from a Difficulty of 6, and if we succeed on the roll, we can get them to do something inconvenient.
But wait! It's reasonable for us to assume that this servant would be severely punished if they spilled the family secrets to some suspiciously anathematic strangers, so this actually needs not one, but two repurchases of the Persuade for 2 successes each. (One repurchase would get them to do something risky, but not risky enough to pose a threat to their livelihood - and in this scenario, "your employment is terminated" is one of the least bad things that could happen to them.)
So we need to roll 10 successes to intimidate this dude! Oh no!
Luckily, the ST accepts our proposal that "I prefer to avoid grievous bodily harm at the hands of the Anathema whenever possible" should really be worth at least a Minor Intimacy on the sheet of the average person, so the difficulty goes down to a much more manageable 8. Sadly, being the kind of dum-dum whose investigative technique is limited to making Jack Baueresque faces while shouting "WHERE IS THE BOMB" very intently, we still fail.
However, this does not stop us from attempting to make more social influence actions in the same scene, so now we try a Read Intentions to suss out what the goal of our target is here. Luckily, Read Intentions is never modified by the target's Virtues and Intimacies, so we only need to overcome a base Resolve of 3. We roll a five - allowing us to not only succeed, but also buy the effect of a different social influence action!
We decide we'd prefer to know what our target is up to, before committing ourselves to anything. "He's going to try to kill you, so none of this matters", our ST says with a shit-eating grin.
"Wait, you piece of shit", we complain vigorously. "If he thinks he can kill us so none of this matters, shouldn't trying to get him to tell us where the young mistress is have been an inconvenient task rather than a life-changing one? My previous persuade totally should've succeeded! Well whatever, I use my remaining two successes to buy the effect of Persuading him to do inconvenient task, so he should tell us where she is now."
"Wait, this is bullshit", the ST grumbles. "You can't just bypass opposed Intimacies by using your extra successes on Read Intentions to buy the effects of other social influence actions, this is degeneracy of the highest order."
"Well rules says I totally can", we beam while mentally noting that we shouldn't abuse this too much, otherwise he's gonna raise the issue to the devs on Discord.
"Whatever", he exhales, annoyed. "Asking a character to abandon or ignore their Major Virtue is an unacceptable influence anyways. His Major Virtue is his Loyalty to the family, so the influence attempt is still a no-go."
"Your adventure design is terrible!", we protest. "Antagonists are much more interesting when they aren't just going 'nope' to any influence you're trying to do! Also, how the fuck are we going to illustrate the rules for retrying influence now? Also what about the rules for hard bargains? Or rejecting influence? This example writeup is garbage!"
