I know it's possible to have >100% of shares held via shorts, but how can institutions hold more than 200% of shares?

Your questions have been asked piecemeal in several other questions over the past 2 weeks.

Two reasons have been offered for the short interest exceeding 100%. First, naked shorting and second, a share can be loaned for shorting more than once. The general consensus has been the latter but no one has definitely sourced that. So it stands to reason that if a share can be loaned more than once then the short interest can exceed 100% and ownership can exceed 200%.

Understand that when share are shorted, it creates a synthetic long share. IOW, owner (A) of 100 shares loans the shares to (B) for shorting and (C) buys them. The end result is 100 synthetic long shares (A), 100 short shares (B), and 100 long physical shares (C) for a total of 200 long and 100 short. If this was repeated again, it would become 300 long and 200 short.

Another question has been making sense of the numbers posted at Yahoo Finance, FINRA, et al. While some of the stats calculated makes sense, others haven't added up and no one has reconciled them.

So all I can suggest is that you take the synthetic longs into consideration when you do your calculations and if they don't make sense, welcome to the club.