Cloud multi-tenancy is typically constrained to a single interactive service colocated with one or more batch, low-priority services, whose performance can be sacrificed when deemed necessary. Approximate computing applications offer the opportunity to enable tighter colocation among multiple applications whose performance is important. We present Pliant, a lightweight cloud runtime that leverages the ability of approximate computing applications to tolerate some loss in their output quality to boost the utilization of shared servers. During periods of high resource contention, Pliant employs incremental and interference-aware approximation to reduce contention in shared resources, and prevent QoS violations for co-scheduled interactive, latency-critical services. We evaluate Pliant across different interactive and approximate computing applications, and show that it preserves QoS for all co-scheduled workloads, while incurring a 2.1% loss in output quality, on average.