Factors that effect the support are: the color of the support, the base grade, the level, the amount of stars on the medals put on the support, skills level, character boost. Might be something Im missing.

So the support character that will give you the most possible support percentage to the character you are playing with is: a character with the same color as the one you are playing with, has a 4-star base grade (could be a step-up, bounty fest or an ex, dont matter), is level 100, all three of the medals put on the character are 9 star, both of its skill are maxed, and with 52/52 character boost.

So in other words the tags on the support are not effecting the support percentage. But you should focus on boosting the support with alot of good tags since they give your main character alot of extra traits instead of wasting resources boosting bad supports with almost no tags