Need an algorithm to optimize benefits (...

The following applies to US health insurance policies:

1. Dual/multiple coverage from work means dual/multiple premium payments, either out of the employer's or the employee's pocket, or more likely than not, a combination of both.
2. When registering with a health provider to receive service, a patient is required to furnish complete insurance information, which includes coverage from dual/multiple policies if applicable.
3. Coordination of benefits in dual/multiple coverage is the responsibility of the claims department of insurance companies.
4. Indeed, per federal law, one can add (and drop) coverage in any of a number of life status change events, of which loss of employment is one (the others are birth of child, death, marriage, divorce, adoption, etc.).
5. In the final analysis, whether or not to opt for dual/multiple coverage when the opportunities present themselves depends on one's individualized benefit optimization algorithm (maximize benefist/minimize costs): Usually, premium payments for dual/multiple policies will not be offset by the co-pay/co-insurance savings from dual/multiple coverage (exceptions exist in cases of serious illnesses or high co-insurance payments); and, it is worth keeping in mind that even with policies where the employer pays 100% of premium, the cost incurred to the employers in dual/multiple coverage are likely much higher than the savings the employee will ever realize.
6. Since my wife and I - knock on wood - don't have serious health issues in the family, we have single medical coverage only although we are fortunate enough to have the opportunity to opt for dual coverage (we do have dual dental coverage, though, but that is due to other considerations, namely, kids who may soon need orthodontic service).