If I want to say "I can" in Latin, I will usually use posse. But what if I want something stronger and more emphatic, like "I am capable of", "I am able to", or similar? I am not aware of a Latin idiom that would mean more or less the same as posse but have more gravity. Are there classical attestations of an "emphatic posse" that I could mimic?
One sometimes finds valere + infinitive used with the sense of 'to have the ability or power to' (OLD definition 6). I'm not sure it really has more gravity than posse; at any rate, I tend to think that the mere fact that it's being used instead of the more obvious posse makes it somewhat 'marked' in the sentence.
Your only real option is to use word placement, that is to put the [posse] form in an unusual position in the sentence. It's quite a normal way of emphasising : for example, where magnum pondus tollere potest simply indicates the ability to lift a large weight, potest magnum pondus tollere is a stronger declaration of it.
Otherwise, there are such phrases as nequeo quin …, 'I can't do other than …*, to suggest you can do something, but only because you have no alternative (this may get fairly close, but it isn't really what you want), and haud dubitandum erat quin possem …., 'there was no doubting but that I was able to … ', which might serve well enough.
There is also the Latin proverb often attributed to Hannibal when he attempted to cross the Alps: viam aut inveniam aut faciam (I shall either find a way or make one) which although not using posse may be a suitable replacement for 'I can' depending on the context.