Is there overlap between personal hospital insurance plan & company employee hospital insurance plan if both are offered by same insurer?

There's likely to overlap since they are all hospitalisation plans but the company's insurance policy terminates when you are no longer in the company. So, just get your favourite plan.

Hospitalisation plan cover for expenses due to treatment costs in the event of an injury, illness or disability. Since you have your company coverage, there will definintely be overlap coverage if you choose to purchase private shield coverage.

For example, let say the hospital bill is $20k and it can be fully cover by your company insurance, then the private shield coverage will not be able to claim because you have fully claim. But if the hospital bill is $200k, your company coverage can claim up to $80k, then the remainng $120k can be claim from the private shield plan.

Having said that above, your company policy may end when you change employer or retire, so you should have a personal hospital insurance policy as well. Do not wait until you stop working to buy a personal hospital insurance policy. By then, you may not be insurable due to age or poor health.