Then Geo’s point that Storyline Standing is not shared stands. Storylines give Faction standing and that can only be improved for each character individually, not by fleet sharing.
You basically have to accept normal missions with all chars and run storylines on all chars that need better faction standing.
You can also run The Blood-Stained Stars - EVE University Wiki together with all alts parallel then share among all three (not sure if it is better to not share and then the total is different for the owner so check about that first but even then easier to run them together than one by one).
It gives a considerable standings boost for a chosen empire faction and can be run again 3 months after finishing the prior one.