No. Small claims are for claims which are small. This belongs in civil court all at once and you don't get to go in with the sheriff (if you win) unless they are ordered to pay you and refuse to.
There are explicit rules against claim splitting and you risk either the judge combining all of your filings into one case and moving it to a different court or dismissing all of the claims after the first one. There are very good reasons why a person can't keep suing you over and over for the same event.