Suppose you have 4 samples; let's label them A, B, C, and D. Sample A has genotype T/T at this SNP, and phenotype value 175. Sample B has genotype C/T and phenotype value 160; sample C has genotype C/C and phenotype value 155; and sample D has genotype T/T and phenotype value 173.

A standard GWAS is based on [phenotype] ~ [genotype, intercept, other predictors] regressions. Ignoring "other predictors" for now, the data matrices for the regression at this SNP would look like

phenotype        intercept  #C
      175                1   0
      160                1   1
      155                1   2
      173                1   0

I've labeled the single genotype column "#C" here, representing "number of copies of the C allele".

Now change sample D's genotype to A/T. This would leave the original data matrices unchanged: neither A/T nor T/T have any copies of C. Which may actually be fine for detecting whether the C allele has a noticeable effect, but we're now also interested in whether the A allele does. We investigate that by adding a #A column:

phenotype        intercept  #A  #C
      175                1   0   0
      160                1   0   1
      155                1   0   2
      173                1   1   0

Of course, with only 4 samples, we can't conclude much. But (with a good choice of "other predictors") this approach becomes quite effective as your sample size increases.