Final answer:
The Independent Practice Association (IPA) HMO offers the most flexibility for physicians, allowing them to maintain private practices and accept both HMO members and non-HMO patients, thus providing the greatest autonomy.
Step-by-step explanation:
Among the types of Health Maintenance Organizations (HMOs), the Independent Practice Association (IPA) offers the most flexibility for participating physicians. Unlike a closed-panel HMO where doctors are typically employees of the HMO and only see its members, or a group-model HMO where physicians are part of a group that contracts with the HMO, the IPA allows doctors to maintain their own practices and see non-HMO patients as well. This arrangement provides greater autonomy and the possibility to balance between patients on the HMO plan and those with other forms of insurance or payment. The open-panel HMO, while also allowing doctors to see non-HMO patients, often places more restrictions on physician participation than an IPA does.