In General Insurance, which includes Health Insurance, the coverage is based on Indemnity Insurance. Ie, you can only be insured upto the amount of loss/ expense. Even if you have more than one policy, each will pay you their proportionate share of the SUM INSURED (SI) upto the level of loss/expense or the SI.
Life Insurance (eg, Term Plan), is based on Benefit Insurance, since Life is actually priceless, though theoretically monetarily, upto your HLV. Hence, even if there are more than one company, each will pay the full amount of the SUM ASSURED as per your policies. That's why their Underwriters are careful that they take all your insurances into consideration, before accepting your Proposal.
