The clinical use of amide proton transfer (APT) imaging is hindered by long scan times. Accuracy generally limits the use of conventional sensitivity encoding (SENSE) methods in APT, to an acceleration factor of 2. A novel variably-accelerated sensitivity encoding (vSENSE) method can provide more accurate results and therefore substantially higher overall acceleration factors than conventional SENSE. Here, vSENSE is further developed to eliminate the requirement that one fully-sampled APT frame be acquired, and extended to three dimensions (3D). Furthermore, we combine vSENSE with parallel transmit saturation, and apply it proactively to three normal volunteers and eleven patients with brain tumors.