Contrast treated samples against both scramble and untreated controls

Hi there, I am using DESeq2 to analyse RNAseq from siRNA treated samples and 2 controls (Scramble and Untreated). Each treatment has 4 cell lines:

   treatment cellline group
   <fct>     <fct>    <fct>    
 1 Untreated  1       Control     
 2 Scramble   1       Control     
 3 Knockdown  1       Knockdown  
 4 Untreated  2       Control     
 5 Scramble   2       Control     
 6 Knockdown  2       Knockdown
 7 Untreated  3       Control     
 8 Scramble   3       Control     
 9 Knockdown  3       Knockdown  
10 Untreated  4       Control     
11 Scramble   4       Control     
12 Knockdown  4       Knockdown

I would like to contrast Knockdown versus all Control samples but remove effects due to (i) cell line and (ii) scramble. I would like to use the most optimal design and contrast to achieve this.

The straight forward options are to either lump together Untreated and Scramble into a single Control group:

design = ~ cellline + group
results(dds, contrast=c("group", "Knockdown", "Control"))

or ignore Untreated samples all together:

design = ~ cellline + treatment
results(dds, contrast=c("group", "Knockdown", "Scramble"))

Neither are optimal and I wondered whether there is a better option that incorporates Scramble treatment into the design but avoid the error: model matrix is not full rank, so the model cannot be fit as specified. For example, could i specify a likelihood ratio rest with the full model = ~ cellline + treatment + group and reduced = ~ cellline + treatment?

Many thanks!

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