It's a fractional program under FAR 91 Subpart "K", and yes they have "op-specs" like a Part 135 program.
91.1001 Applicability
(8) Fractional ownership program management services or program management services mean administrative and aviation support services furnished in accordance with the applicable requirements of this subpart or provided by the program manager on behalf of the fractional owners, including, but not limited to, the—
(i) Establishment and implementation of program safety guidelines;
(ii) Employment, furnishing, or contracting of pilots and other crewmembers;
(iii) Training and qualification of pilots and other crewmembers and personnel;
(iv) Scheduling and coordination of the program aircraft and crews;
(v) Maintenance of program aircraft;
(vi) Satisfaction of recordkeeping requirements;
(vii) Development and use of a program operations manual and procedures; and
(viii) Application for and maintenance of management specifications and other authorizations and approvals.
91.1001 Applicability
(8) Fractional ownership program management services or program management services mean administrative and aviation support services furnished in accordance with the applicable requirements of this subpart or provided by the program manager on behalf of the fractional owners, including, but not limited to, the—
(i) Establishment and implementation of program safety guidelines;
(ii) Employment, furnishing, or contracting of pilots and other crewmembers;
(iii) Training and qualification of pilots and other crewmembers and personnel;
(iv) Scheduling and coordination of the program aircraft and crews;
(v) Maintenance of program aircraft;
(vi) Satisfaction of recordkeeping requirements;
(vii) Development and use of a program operations manual and procedures; and
(viii) Application for and maintenance of management specifications and other authorizations and approvals.