I obviously lack some context here, but just based on this one sentence, I would interpret it as follows:
The tool only supports (is trained on) data in which the reference base is present on both alleles (e.g. A/A), is heterozygous (e.g. A/G) or homozygously alternative (e.g. G/G) - that is allele frequencies of 0, 0.5 or 1.
In somatic data, mutations accumulate over time, so unless it is a single-cell sequencing, you might find more than two genotypes for a particular SNP, e.g. 60% C, 35% T and 5% A or whatever.
The "any other samples where the genotypes go beyond two copies of DNA" refers to any cell, that is not or no longer diploid. This may happen in humans through Copy Number Variations (CNVs) in e.g. cancer. In other organisms, a different ploidy is quite common: The Marbled crayfish for example is triploid (has three copies of its genome in each cell) and plant genomes are notorious for having high ploidies (some cultivars of berries up to >25, I believe). Some flies such as Drosophila are capable to selectively amplify chromosomes (polytene chromosomes) and can generate a few thousand copies within a single cell.
All of those cases obviously are very challenging for variant calling, as it is unclear if an infrequent base call represents a sequencing error or indeed a valid biological occurrence.