Collinearity in logistic regression

Suppose we are designing a case-control trial to test the effectiveness of vaccine 1 for a certain disease. 50% of the subjects who are vaccinated with vaccine 1 are vaccinated with vaccine 2, which is intended for the same disease, while only 20% non-vaccine 1 recipients are vaccinated with vaccine 2. The reason they are recommended to be vaccinated sequentially is both of them have distinctive benefits. Is it preferable to restrict the analysis population to vaccine 2 free subjects (and increase the study size) or just perform logistic regression adjusting for vaccine 2 (and including interaction term ) ? Does the percentage of vaccine overlap (50% in this example) impact the preferred approach?**