Background Many genetic variants have been identified in the human genome. The functional effects of a single variant have been intensively studied. However, the joint effects of multiple variants in the same genes have been largely ignored due to their complexity or lack of data. This paper uses HMMvar, a hidden Markov model based approach, to investigate the combined effect of multiple variants from the 1000 Genomes Project. Two tumor suppressor genes, TP53 and phosphatase and tensin homolog (PTEN), are also studied for the joint effect of compensatory indel variants. Results Results show that there are cases where the joint effect of having multiple variants in the same genes is significantly different from that of a single variant. The deleterious effect of a single indel variant can be alleviated by their compensatory indels in TP53 and PTEN. Compound mutations in two genes, β-MHC and MyBP-C, leading to severer cardiovascular disease compared to single mutations, are also validated. Conclusions This paper extends the functionality of HMMvar, a tool for assigning a quantitative score to a variant, to measure not only the deleterious effect of a single variant but also the joint effect of multiple variants. HMMvar is the first tool that can predict the functional effects of both single and general multiple variations on proteins. The precomputed scores for multiple variants from the 1000 Genomes Project and the HMMvar package are available at https://bioinformatics.cs.vt.edu/zhanglab/HMMvar/