A group life insurance policy sponsored or paid for by your employer may not be sufficient to provide financial security to your family if you should die. But the limitations of group life insurance are only the beginning of the answer, because you have a use for multiple policies of different types and lengths that a standard group life insurance policy is not able to provide for.
A group life insurance policy does not take life events into consideration. For example, if you have children who you want to attend college after they graduate, a portion of your group life policy could be used, but since there is a definite time limit involved, this type of policy is not an ideal solution. Instead, you should compare term life insurance quotes to compare policies that can provide coverage for such events as college tuition, paying off the home mortgage, or other uses where the need for the policy will expire after a given number of years.
Group life insurance may not have the financial tools built into it that a regular whole or universal life policy includes. A whole life policy that you purchase yourself includes a cash accrual that you can borrow against without collateral or intense credit scrutiny. And a universal life policy has the potential for even more financial gains by allowing you to manipulate how the accrued cash is invested. Because these types of policy have advantages you can use while you are still alive without affecting the payout when you die, having one or more such policies is a good idea for the long haul.