Would I be able to double claim from my hospitalization insurance?

Generally, there are two types of insurance payout when you buy them

(1) Sum assured - these are assured amounts that should any of the conditions are met, they payout the coverage that is in the contract. These are commonly life insurance / CI insurance / Disability insurance

(2) reimbursement - more commonly in the insurance industry, which spans from general insurance to building insurance, hospitalisation and accident. These only payouts with claims (which is meant to bring you back to the original state).

So on your point about "double claim", buying a few policies allow you to claim from different parties. But they will share the cost of the insurance together (at their own discussion). You will be reimbursed based on the coverage each one cover. They are able to fill the gap if you bought multiple ones with different policy wordings.

What is common over here is if you have corporate and personal, they will complement each other in their coverage. I would not go into portability as some have mentioned.

In short, reimbursement is different from the sum assured, and you will only be reimbursed the total lost, and not "profit" from double claim.

Now to add on with some information that doesn't directly answer the question:

You may now be tempted to then not purchase a personal hospitalisation insurance due to several reasons:

"I already have a plan with my company what? Why need another one"

And some things for you to consider if you were to decide on whether to keep your personal hospitalisation insurance:

Portability of corporate insurance: While some company insurance is portable even when you leave the company, most of them laspe once you leave the company. Example – the Transferable Medical Insurance Scheme which is a group insurance that has inpatient coverage up to a maximum period of 12 months when an employee leaves his employment.

Coverage of corporate insurance: Most corporate insurance will have claim limits imposed on them. In the unfortunate scenario where you reach your claim limit of your corporate insurance, you will be left to deal with the expenses alone.

Retirement plans: If you intend to retire with a hospitalisation plan, get your own one. Your company likely will not cover for you once you retire.