[Boromir88]

The Ring is still giving them power according to their stature, yet it is also increasing this same 'stature'. I would believe that, should someone be able to hold on to the Ring, use it and avoid meeting Sauron head-on at once, they would become more powerful than Sauron himself (by gaining mastery of the Ring). But in order to gain mastery of the ring they would have to become so corrupted that they'd be just another Sauron.~Farael

The thing is it's not as easy as being able to hold on to the Ring for a long amount of time. It deals with breaking the bond between the Ring and Sauron and to do that you have to be extremely powerful...

While he wore it, his power on earth was actually enhanced. But even if he did not wear it, that power existed and was in 'rapport' with himself: he was not 'diminished'. Unless some other seized it and became possessed of it. If that happened, the new possessor could (if sufficiently strong and heroic by nature) challenge sauron, become master of all that he had learned or done since the making of the One Ring, and so overthrow him and usurp his place.~Letter 156

Saruman had attempted to do exactly as this says...become master of all that he had learned or done since the making of the One Ring, and so overthrow him and usurp his place...whether he would have been successful is up to debate. We know that Saruman was well learnt in the Rings of power, especially the One Ring. His plan was to buddy up to Sauron, be patient, wait for the perfect moment, and then turn on him, using the Ring against him (see Gandalf's account of Saruman in The Council of Elrond). Whether he would have been able to do it is up to debate. Personally, I believe Saruman was fooled by his own capabilities and his own power, and would have failed.

The Ring's powers and Sauron's powers were one. He had poured so much of his own power in it, the Ring was bound to him. In order to break the "bond" and diminish Sauron one had to do as it says in the quote above. And as we see from Letter 246, Tolkien thinks only Gandalf would be able to do so:

In any case a confrontation of Frodo and Sauron would soon have taken place, if the Ring was intact. Its result was inevitable. Frodo would have been utterly overthrown: crushed to dust, or preserved in torment as a gibbering slave. Sauron would not have feared the Ring! It was his own and under his will. Even from afar he had an effect upon it, to make it work for its return to himsefl. In his actual presence none but very few of equal stature could have hoped to withhold it from him. Of "mortals" no one, not even Aragorn. In the contest with the Palantir Aragorn was the rightful owner. Also the contest took place at a distance, and in a tale which allows the incarnation of great spirits in a physical and destructivle form their power must be far greater when actually physically present. Sauron should be thought of as very terrible. The form that he took was that of a man of more than human stature, but not gigantic. In his earlier incarnation he was able to veil his power (as Gandalf did) and could appear as a commanding figure of great strength of body and supremely royal demeanour and countenance.

Of the others only Gandalf might be expected to master him - being an emissary of the Powers and a creature of the same order, an immortal spirit taking a visible physical form. In the "Mirror of Galadriel", it appears that Galadriel conceived of herself as capable of wielding the Ring and supplanting the Dark Lord. IF so, so also were the other guardians of the Three, especially Elrond. But this is another matter. It was part of the essential deceit of the Ring to fill minds with imaginations of supreme power. But this the Great had well considered and had rejected, as is seen in Elrond's words at the Council. Galadriel's rejection of the temptation was founded upon previous thought and resolve. In any case Elrond or Galadriel would have proceeded in the policy now adopted by Sauron: they would have built up an empire with great and absolutely subservient generals and armies and engines of war, until they could challenge Sauron and destroy him by force. Confrontation of Sauron alone, unaided, self to self, was not contemplated.

So, here we see that any mortal who attempts to withold the Ring from Sauron, and master it, would not be able to do so. Gandalf is only the person that may possibly be able to master Sauron and the Ring.