Suikoden IV could have used III's multiple storylines in that aspect. Snowe is... a passing character, to say the least.
I'd really advise against going 4-5-1-2-3 ... 4 is dreadful, 5 is very long and kinda expects you to behave in a certain way 4 doesn't teach you, 1 and 2 will be too basic in comparison and 3 is the gameplay outcast. Playing in their numerical order let's you explore the largest events on 1-2-3, and then 4-5 makes you dive into the lore of events already mentioned. Not to mention people like Jeane or Vicky that don't fit storyline-wise. Yeah, play them in order.
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