Which company can apply to the commissioner for a license to conduct various types of insurance except for specific lines?

A captive insurance company is a type of insurance company that is formed to insure the risks of its parent company or group of affiliated companies. While these companies can indeed apply for a license to conduct various types of insurance, they typically focus on specific lines that are associated with the risks of their parent organization.

The context here highlights that captive insurance companies provide a tailored approach to risk management for their affiliated entities rather than offering broad insurance coverage across all lines. This includes advantages such as more control over their insurance costs and the ability to cover unique risks that are specific to their business operations.

The other organizations mentioned, such as fraternal benefit societies, stock insurance companies, and reciprocal exchanges, have different regulatory frameworks and are more likely to be involved in providing a wider range of insurance products to the general public, rather than focusing on the specific risks of a limited group of insureds. Therefore, the captive insurance company stands out as the correct answer due to its unique regulatory position and focus on limited lines of insurance.