This paper introduces the common coil magnet system for the proposed very large hadron collider (VLHC) [11. In this system, the high energy booster (HEB), the injector to VLHC, is integrated as the iron dominated low field aperture within the coldmass of the common coil magnet design introduced earlier [2]. This 4-in-l magnet concept for a 2-in-l machine should provide a major cost reduction in building and operating VLHC. Moreover, the proposed design reduces the field quality problems associated with the large persistent currents in Nb,Sn magnets. The paper also shows that the geometric field harmonics can be made small. In this preliminary magnetic design. the current dependence in harmonics is significant but not umnanageable.