We know Hashem can influence man to sin. Omnipotence.
The question is: Would He?
There are different approaches to what happened with Par'oh.
The Rambam says that yes, Hashem will take away the possibility of teshuvah. This is a potential punishment for sin, if the sin is egregious enough. So, what happened to Par'oh could happen to others. Hilkhos Teshuvah 6:3:
אפשר שיחטא אדם חטא גדול או חטאים רבים עד שיתן הדין לפני דיין האמת שיהא הפרעון מזה החוטא על חטאים אלו שעשה ברצונו ומדעתו שמונעין ממנו התשובה ואין מניחין לו רשות לשוב מרשעו כדי שימות ויאבד בחטאו שיעשה.
It is possible for a person to sin a great sin or many sins until the judgment is placed before the True Judge that the payment should be upon the sinner for those sins which he did by his own will and knowledge. That they withhold from him teshuvah, and do not give him permission to return from his evil, so that he should die and be lost with the sin that he will do.
Rav Yisrael Salanter (Kokhevei Or 79) quotes this Rambam, as part of defining three levels: Hashem helps most people do teshuvah. For particularly bad sinners, Hashem arranges life such that he doesn’t have opportunity. And finally, the Rambam’s level that even the ability itself is taken from the sinner.
I would take R Yisrael Salanter as saying that Hashem does not assist with this miracle in allowing teshuvah to happen for the evil, and keeps this miracle altogether from the truly evil. But why not? “Lo chafotz bemos hameis, ki im beshuvo midarko vechayah — [Hashem] does not desire the death of the dead, but that he return [does teshuvhah] from his way and live.” Hashem Himself prefers teshuvah!
I think (the Rambam and RYS don’t say or imply the following, it’s just my conjecture) that we are referring to the sinner who so internalized his evil that such a change would be a change in the person’s essence, not some incidental attribute. Par’oh couldn’t do teshuvah because at that point, a post-teshuvah person wouldn’t be Par’oh anymore. The only way his soul could be redeemed is through the process of punishment in the afterlife.
More personal creativity... We could explain the Rambam using Rav Eliyahu E Dessler's concept of the Nequdas haBechirah (the Decision Point). It is a model of free will that speaks to me because it is in accord with how it feels like to me, subjectively. Most options don't even become decisions. How many of us go into a store and make a real decision not to shoplift that nice watch? For some people that's a battle. For others, it all happens without conscious thought. But, for someone else what takes thought is how honest to be on their income tax forms. All of us have these battlefronts, where the conflict requires actual decision making. And with each decision, for good or evil, moves that battlefront over, making the next decision that much quicker.
It is possible the Rambam simply meant that Par'oh got himself to a place where doing teshuvah would never cross his mind. It was outside the realm of his free will. The Rambam, after all, would be very content to take that kind of rational and causal approach to reward and punishment.
On the other hand, the Ramban and Seforno (on Shemos 9:35) consider Par'oh's case to be a special one. Par'oh was already subjected to supernatural influence, in the form of living through all those makkos. Had Hashem let him do teshuvah because of the influence of miracles, that would have been a distortion of this free will. Hashem blocked his heart from being influenced by miracles, thereby keeping the scales at the balance they would have had otherwise.
I just realized I wrote yet another harden Par'oh's heart answer. Adding that one approach would mean Hashem would do it again and the other that Par'oh's case was unique probably doesn't justify it.