Id make a distinction between characters that that help out their team mates and characters who's main function is support.
Spider Man is not really a support character. Its not really his gig.
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It took a while to find the name .. but ..
Xmen Elixir would be a good example. He is basically a healer, heals by touch. That's all he could do at first. Turns out he can also harm by touch, and he augmented his body some using that process.
So he is support, fights in melee only, has some limited durability, and tries to keep a low profile.
Very similar to this Guardian idea.