I have ~300 samples (RNA-seq) with a desired design matrix as: ~ Strain + Condition + Strain:Condition

Unfortunately this is an underdetermined system, as Strain can take one of 28 values, and Condition can take on one of 12, so the inclusion of the interaction terms gives me more variables than I have data.

In general linear models, one way to overcome an underdetermined learning problem is to apply constraints to to the number of non-zero parameters such as the Lasso.

Is there something akin to this in DESeq2?

No we don’t have L1 penalties. We do something like ridge (L2) but in an empirical Bayes setting not in a cross validation setting. You can take a look at glmnet:

https://cran.r-project.org/package=glmnet