You can use the built in task agent. When you have a plan and ready for Claude to implement, just say something along the line of “begin implementation, split each step into their own subagent, run them sequentially”
I'll admit it's a bit insane to have it make changes in the same directory simultaneously. I'm sure I could ask it to use git worktrees and have it use separate directories, but I haven't (needed to) try that (yet), so I won't comment on how well it would actually do with that.