Amount of Sum Assured admissible in a Term Insurance, depends on your earning capability during the "earning years of your life span", less your liabilities and personal expenses, ie, what would be available for your dependents. This is referred to as your Human Life Value.
Even if you take more than one company's Term Plan, all insurance Companies will ask you for details of existing life insurance coverage, as also your income details. In case someone wants a coverage beyond his HLV, it will not be admitted by the Underwriters.
If you are thinking about diversification in you risk mitigation efforts, it is not of major concern. IRDAI ensures that NO policy can be brought into the market, unless the insurers have a Solvency Ratio of minimum 150% ( ie, 1.5 times the money required to settle claims even in the event of a large scale calamity).
More the policies, more the paperwork and running around for your heirs.