I think St. Thomas Aquinas proved God’s omnipotence using reason alone in the Summa Contra Gentiles Book 1:
“the mode of a thing’s excellence is according to the mode of its being. For a thing is said to be more or less excellent according as its being is limited to a certain greater or lesser mode of excellence. Therefore, if there is something to which the whole power of being belongs, it can lack no excellence that is proper to some thing. But for a thing that is its own being it is proper to be according to the whole power of being. … God, therefore, Who is His being, as we have proved above, has being according to the whole power of being itself.”
It seems to follow from this that any possible power must be in the nature of God. And I don’t think that’s any different from being omnipotent.
There is a similar argument in the Summa Theologica:
“As stated above (Article 1), active power exists in God according to the measure in which He is actual. Now His existence is infinite, inasmuch as it is not limited by anything that receives it, as is clear from what has been said, when we discussed the infinity of the divine essence (7, 1). Wherefore, it is necessary that the active power in God should be infinite. For in every agent is it found that the more perfectly an agent has the form by which it acts the greater its power to act. For instance, the hotter a thing is, the greater the power has it to give heat; and it would have infinite power to give heat, were its own heat infinite. Whence, since the divine essence, through which God acts, is infinite, as was shown above (Question 7, Article 1) it follows that His power likewise is infinite.”
Is that helpful?