Thanks, ATpoint. But I'm not sure if I understand your suggestion. Are you suggesting the following design?
| sample_name | treatment | RNA_extraction_day | library_prep_day | merged_days |
| ----------- | --------- | ------------------ | ---------------- | ----------- |
| S1 | con | A | C | A_C |
| S2 | con | A | C | A_C |
| S3 | con | B | D | B_D |
| S4 | con | B | D | B_D |
| S5 | stage_1 | A | C | A_C |
| S6 | stage_1 | A | C | A_C |
| S7 | stage_1 | B | D | B_D |
| S8 | stage_1 | B | D | B_D |
| S9 | stage_1 | B | D | B_D |
| S10 | stage_2 | A | C | A_C |
| S11 | stage_2 | A | C | A_C |
| S12 | stage_2 | A | C | A_C |
| S13 | stage_2 | B | D | B_D |
| S14 | stage_2 | B | D | B_D |
| S15 | stage_2 | B | D | B_D |
| S16 | stage_3 | A | C | A_C |
| S17 | stage_3 | A | C | A_C |
| S18 | stage_3 | A | C | A_C |
| S19 | stage_3 | B | D | B_D |
| S20 | stage_3 | B | D | B_D |
In my head, the model ~ treatment + merged_days would probably give me a full-rank model matrix :)