Having overlapping health insurance can be tricky. Since insurance companies will want to know what other providers you are receiving benefits from, the most common situation that develops is that both insurers attempt to deny the claim on the grounds that other company is responsible. If you are going to have multiple health insurance policies, be sure that they complement each other instead of duplicating coverage's.
Insurance companies have a right to know whether another insurer in involved. This reduces fraud for both companies, both on the part of patients and dishonest filings by healthcare providers. Since you cannot legally claim more for services than they actually cost, claiming the same procedure under two different policies would be illegal and prosecuted by the insurance company. Fraud is a serious offense for insurance companies, and results in millions of dollars paid out in any given year, making it vital for insurers to track and prosecute fraudulent activity whenever it is discovered.
Where having two policies works to your advantage is when one policy fills gaps in the other. For example, one policy may not cover a specific type of treatment, or excludes medical equipment, while the other policy covers the equipment but does not include the hospital visit before you go home. Another example would be when your hospital stay is longer than the primary policy covers, and the secondary policy only kicks in when the primary coverage is exhausted.
It is okay to have multiple health insurance policies, but you must list them when asked to do so by each company. Commonly, people have separate policies for primary care, dental care, and prescription coverage, along with any supplemental plans that fit their needs. They key is that additional health insurance plans work together without conflicting. As long as the two policies provide complementary coverage, they are working for you best interest, but once a conflict is introduced, you may be on the road to an insurance nightmare.