MTI can certainly be reduced by the above-mentioned thoughts. There are distinct variants, as mentioned, in the way a person from North India communicates versus a person from South India. Again, the people from the Eastern parts of India tend to elongate their vowel sounds and use intonation more. This can be seen in stark contrast to the flatter tones of, say, someone from the South.
When we train corporates, we first work on their existing MTI to make them more comprehensible to us, then take them to the next level, for want of a better term, 'Global English.'
Imitation is certainly one way to learn, as mentioned by the above user. I'd like to point out, though, that unless someone is raised in a particular country or has resided there for many years, or is especially gifted with languages, it's possible to distinguish that the particular person is not a native speaker. I've heard this often from many people, 'His/her English is so good. He sounds almost British but isn't.' The same can be applied to American accents. The simple reason is this: no matter how much we learn and imitate and reduce our MTI, there are certain nuances that will distinguish a native speaker from a person who learns it out of passion or requirement.
This is not to disappoint anyone, but rather to own it. One can reduce MTI, one can sound different, global, international (insert any adjective). However, one cannot sound completely like a pure Brit or American, unless, again, we belong to the above-mentioned categories.