Realistically speaking? Only those regions that India is claiming from China, plus any bits and pieces which they see convenient to take away from China that would give their military better geographical advantage over the PLA.
I think I have to add this on top of what I have said - Despite how the hubris by the Indian populace and politicans, smart and rational people in the higher levels of the Indian government still do exist, and I believe this extends to the higher levels of the Indian military as well.
Sure, having the Indian military doing deep infiltration into Tibet to station agents is definitely possible - Nobody can guard the entire length of the Sino-Indian border anyways. However, we all know that the Indian military is going to be served with HELL if they ever wish to fight their way across the entire Himalayan and Tibetan mountain ranges, so just forget about them taking Lhasa. Plus, the PLA would definitely blow up mountains and hills to halt their advances in the mountains, so I don't believe that there would be genuinely stupid higher-level commanders in the Indian military that would try that.
Therefore, for India opening a new front against China in the Himalayas, their main goals would be to:
1. Take over territories which they see as belonging to themselves + some extras,
2. Split China's attention away from Taiwan, AND
3. Keep considerable number of PLA troops, weapon platforms and equipment tied down on the Himalayan front and the Western Theater Command, therefore restricting their effectiveness into providing assistance to their forces fighting in Taiwan and the WestPac.
Notice how I bolded the #2 and #3, and set a bigger font size for #3. Those are going to be the major objective for a coordinated QUAD assault on China. To play its part in the QUAD, the Indian military just need to keep certain portions of the PLA busy with them and not being able to meaningfully contribute towards their war efforts on Taiwan, while the US, Japan, Australia and the rest of the Five Eyes would do the rest. In fact, there is no need for the Indian military to march towards Lhasa at all - They just need to present enough of a threat for the PLA to respond accordingly.
With large amount of PLA manpower and equipment already dedicated on the WestPac frontier, PLA would only have enough manpower and equipment to push the Indian forces out of Chinese territories, and, at most, reclaim all lost territories that India has taken from China from previous wars and skirmishes. The PLA certainly wouldn't have enough to continue with the invasion of the Indian proper, and that's something that New Delhi definitely knows.