Mediassist HIS (Health Insurance)

I am currently working with TCS but am planning a switch. Both of my parents are suffering from multiple chronic health conditions including cardiac and diabetes. I have currently enrolled them in the company's HIS and unfortunately this entire year a substantial amount of the coverage has been utilised. I feel I was fortunate to be with TCS and have my parents covered otherwise would have been a huge financial jolt to my family. Considering the expansive coverage of the HIS policy and low effect on premium due to pre-existing diseases I wish to know about the various Health Insurance across companies including MNCs, mid sized organisations and start-ups.

Also question to TCS folks, can we continue the policy after leaving TCS by paying a higher premium? And would the coverage and network be same as that for a TCSer?