Ok, I often hear my American teacher says "I am more than happy to help you".
I am not sure it is grammatically correct.
Ok, there is no problem to say "I am happy to help you" or "I am very happy to help you"
But "I am more than happy to help you" sounds quite naturally but does not adhere to the comparative structure.
Why not "I am more happy than many others to help you" which can be explained as:
–I am happy to help you
–Many others are happy to help you
–I am more happy than many others to help you
Best Answer
Yes it is. The comparison here is not that your teacher is happier than others to help you, but that they are happier than "happy".
If we list a number of words that relate to happiness/sadness in order from sadness (a low "happiness" score) upwards, we might get something like this:
By saying "I am more than happy" your teacher means their level of happiness is above "happy" on that scale. Perhaps a more precise way of saying it would be "I am happier than happy to help you", but "more than happy" is a very well established and frequently used turn of phrase.