Quasi-resonant boundary-conduction mode (QR-BCM) and triangular current mode (TCM) have found widespread use in the literature and industry due to their good performance at relatively low complexity. However, additional control challenges occur when these modulations are applied to the four-switch buck-boost (FSBB) converter, due to a discontinuity in switching frequency in multimode operation. This article presents the first closed-loop operation of a variable-frequency, multimode, quasi-resonant BCM control scheme including smooth mode transitions. The proposed control utilizes feed-forward mode transition techniques, based on software interrupt handlers integrated into the digital control scheme. In contrast to most soft-switching schemes in the literature, the proposed digital control does not imperatively rely on high-frequency current measurements but uses dc measurements and high-frequency voltage measurements instead. A 10 kW prototype is developed with which the proposed modulation is compared with three other soft-switching modulation schemes. Our results indicate that the losses of FSBB converter can be reduced by up to 60% using the proposed modulation. Especially at partial powers and high voltages, significant efficiency gains can be achieved.