Can a phenotype only have one allele?
Can there be only one allele at a given locus?

An allele is a variant of a gene. If there is only one allele at a given gene, it means that there is no genetic variance at this specific locus (a locus is a position in the genome. It can typically correspond to a gene). It is not rare at all that the whole population is fixed for the same allele at a given locus. 

Number of alleles

In courses, it is common to consider only the case of 2 alleles. In reality, there might be any number of strictly positive allele. At a given locus, you might have 1, 2, 3 or 11 alleles for examples. The reason why we typically teach about the 2 allele case is that 1 allele is not of much interest as there is not genetic variance at this specific locus and 3 or more alleles makes everything a little more complicated. 

Dominance relationship

In courses, it is also common to consider diploid individuals, 2 alleles and the phenotypes of the three possible genotypes assuming $h_N = 1$ (see here to understand $h_N=1$). In reality, the relationship between two alleles may be vastly more complicated. There is a gradient from complete recessivity to complete dominance (passing through perfect additivity). It is also possible that the heterozygote is more extreme than any of the two homozygotes.

Dominance relationship - Number of alleles

As the number of alleles varies, any pair of alleles have a specific relationship of dominance. While empirical studies suggest that if allele A is dominant over B and B is dominant over C, then A is likely dominant over C, it is not impossible that C could be dominant over A. And again here, I am considering only cases of complete dominance but any scenario is possible.

Dominance relationship - Ploidy

The ploidy also varies from one species to the other (and also from one moment in the life cycle to the other for sexually reproducing organisms). If you have  a polyploid, then the number of possible genotypes is higher than 3 (even for a 2 allele case) and therefore the concepts of recessivity and dominance don't necessarily apply that easily.

Dominance relationship - Epistasis

Finally, there might have interaction between loci making that the relationship of dominance at one locus may depend upon the genetic background (that is the other variants present at other loci). Of course, it may as well depends upon the environment but let's not talk about that for the moment.