This 2015 rodent study investigated interactions of Vitamins A, D, E, and K:

“Significant competitive interactions for uptake were elucidated among vitamin D, E and K, supporting the hypothesis of common absorption pathways:

• Vitamin A – Neither vitamin D nor K impacted vitamin A uptake. Vitamin E significantly improved vitamin A uptake at medium and high concentrations (up to 40%);
• Vitamin D – Uptake was significantly reduced by vitamin E at medium and high concentrations (15% and 17% respectively), as well as by vitamin A at high concentration (30%);
• Vitamin E – Vitamins A and D significantly reduced vitamin E uptake in a dose-dependent manner, while vitamin K had a negative effect only at the highest concentration; and
• Vitamin K – Vitamins A, D, and E significantly decreased vitamin K uptake (from 34% to 58%).

Our data show that vitamin A was mostly absorbed in the mouse proximal intestine, while vitamin D was absorbed in the median intestine, and vitamins E and K in the distal intestine. These results should be taken into account, especially for supplement formulation.”

https://www.sciencedirect.com/science/article/abs/pii/S0308814614013880 “Fat-soluble vitamin intestinal absorption: Absorption sites in the intestine and interactions for absorption” (not freely available)

Subsequent studies have tested this study’s absorption pathway hypothesis, and whether there actually is competition. This study used Vitamin K₁, and I haven’t seen more recent research using K₂ for similar fat-soluble-vitamin pathway analysis.

Regardless, I reserved a late morning time slot an hour after yeast cell wall β-glucan intake and an hour before AGE-less chicken vegetable soup where I only eat walnuts and Vitamin K₂. Current dose is 600 μg of this: