Thank you for your comment. Yes, I'm aware that the order of vaccination might be important. The latest vaccination seems to have the strongest non-specific effects. And live vaccines generally provide other beneficial non-specific effects, such as protection against infections not targeted by the vaccine.

I wrote about this in-detail here: https://medium.com/microbial-instincts/vaccines-have-off-target-non-specific-effects-both-beneficial-and-deleterious-b6a6b1a30081?sk=1bde557020a483ca343415c1eb080225

But there're some caveats. Such data mostly come from lower-income countries with high childhood mortality and are all observational.