I have previously tested for allele-specific expression in paired samples with DESeq2 (like so), but also would like to set up contrasts of ASE across conditions where the sample individual cannot be represented twice. Specifically, I have a dataset where tissue was collect under two treatments (hot v. cold) and would like to identify cases of ASE that are treatment specific. However, since tissues cannot be collected for the sample sample under both "hot" and "cold", I have not been able to get around the issue of this not being a "full rank design"

My condition design table is something like this (with 6 reps of each treatment, so 12 alleles):

ID  treatment   sample  allele
ill98   Warm    1   ref
ill98   Warm    1   alt
ill97   cold    2   ref
ill97   cold    2   alt

Appreciate any guidance on how to set this up in DESeq2 or whether using DESeq2 isn't possible for this purpose! Thank you!

There is a section in the vignette on interactions that will help you here. You want to test for within-individual effects (allele) and compare across group (here treatment) but control for the nested individual effect. See if you can follow the section in the vignette on testing for these effects when individuals are nested within groups.

We've performed these analyses quite a bit lately, and they uncover interesting treatment specific allelic imbalance. I recommend also to examine the counts of genes of interest, while connecting the lines between individuals. You can do this with something like (this may need some tweaking to work):

dat <- plotCounts(dds, gene, intgroup=c("treatment","sample","allele"), returnData=TRUE)
library(ggplot2)
ggplot(dat, aes(allele, count, group=sample)) + 
  geom_point() + geom_line() + facet_wrap(~treatment)