Parasite Eve lets you keep your weapons, for at least the extra game they call EX game or something. I'm not sure if you can just start the main story over with them though. Parasite Eve also had what I thought was a somewhat tricky system of modifying weapons...you had to choose very carefully what elements or features you wanted to add to your guns because you needed an item to perform each modification, you only found a limited number of good weapons with "slots" for these things, and there were only a small number of good traits that you could fit into these slots.
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