Yes. You may assume the role of PI on another investigator's resubmission—just make sure you rewrite the application to reflect that you are now PI and get approval from your business office to make the change. Indicate the change of investigator in your G.210 PHS 398 Cover Page Supplement Form.
In your cover letter, explain why you took over as PI. If the switch is related to comments from the previous review, note that.
See Resubmissions of NIH Applications Questions and Answers for further guidance on this topic.