The adaptation of asexually reproducing organisms is determined by how they accrue beneficial mutations. In large populations, multiple beneficial mutations may arise simultaneously on different genetic backgrounds and interfere with the fixation trajectories of other competing mutations. Multiple mutations interference (MMI) theory has proven useful for investigating these interference patterns. In MMI, beneficial mutations of equal fitness effect arise on a genome with infinitely many loci. However, assuming infinite sites makes it difficult to precisely predict the fates of individual mutations, complicating the detection of MMI in sequence data. In addition, most short-term within-host adaptation of pathogens such as Human Immunodeficiency Virus (HIV) occurs at a limited number of loci under strong selection. For these reasons, we investigate how MMI shapes the genetic composition of a population with few sites under selection. Specifically, we explore the dynamics of multilocus linkage disequilibrium (MLD), a measure of multi-way associations between alleles, in a finite-sites MMI model inspired by early HIV infection. In this regime, MLD oscillates over time in a wavelet-like fashion, a consequence of the sequential acquisition of beneficial mutations. We further show that the frequency of these oscillations is proportional to the rate of adaptation. Together, these findings suggest that MLD oscillations could be used as a signature of interference among multiple equally advantageous mutations.