Why aren't more subtypes of influenza included in the annual vaccine?

If I have understood correctly, each year 3 or 4 specific antigenic varieties are manufactured based on projections. There is also ongoing research based on creating cocktail vaccines where different broad subtypes could be combined.This combination leads to resistance against challenges from subtypes that aren't even included in the vaccine.

My question is why can't they just do this now by giving multiple vaccines, giving people resistance to more than just 3 subtypes? If being introduced to a variety of broad sub-types gives resistance to totally different sub-types, why don't they vaccine people with more than just the three most prevalent antigenic varieties ? Thank you for any answers.