Medicare Part A & B are separate entities than a Medigap plan. Medigap plans are supplemental insurance policies that are used to help cover expenses with your Medicare insurance. Medigap insurance plans are not put out by the government, as Medicare is, nor are any specific brands or carriers endorsed by the government. When you purchase a gap policy you are enhancing your coverage. It will not affect your Medicare Part A & B in any way. The only plan that will have conflict with a gap insurance plan is Medicare Part C. Part C is Medicare Advantage and gap insurance is not required.
You only need to have one gap plan to assist you with your additional insurance needs. Purchasing more than one plan is not only illegal; it is a waste of money. Currently there are 10 separate gap policies available to the public. Each policy offers different coverage as well as has different premiums. Before applying for a gap plan you should carefully review what is offered and what the costs will be for the plan. This will allow you to receive the coverage you need and not purchase too much or too little.
Some states will allow people to purchase gap insurance after there open enrollment period. This is a regulation that is decided by each state individually. However, it should be noted that if you purchase your gap insurance after your open enrollment period you are subject to underwriting clauses that may raise your rates or have pre-existing conditions denied or delayed. If you know you are going to purchase a gap policy you should do so during your open enrollment period. This will save you time and hassle.