I can't find 9, but I figured I'd chime in that abortion cases have been well known to split the court, with the highest number of opinions I could find being 7 or 8 depending on your definition.
Stenberg v. Carhart generated 8 distinct written opinions consisting of a majority opinion with five justices, three concurrences and four dissents. You could count this as 7 though, since Stevens & Ginsburg are in complete agreement, having joined the majority, each other's concurrences and none of the other opinions.
Both Roe v. Wade and June Medical Services, LLC v. Russo generated 6 straightforward opinions.
Planned Parenthood v. Casey created a complex split in the court, I'm just going to quote the syllabus for the detail (PDF link, pgs. 841-842):
O'CONNOR, KENNEDY, and SOUTER, JJ., announced the judgment of the Court and delivered the opinion of the Court with respect to Parts I, II, III, V-A, V-C, and VI, in which BLACKMUN and STEVENS, JJ., joined, an opinion with respect to Part V-E, in which STEVENS, J., joined, and an opinion with respect to Parts IV, V-B, and V-D. STEVENS, J., filed an opinion concurring in part and dissenting in part, post, p. 911. BLACKMUN, J., filed an opinion concurring in part, concurring in the judgment in part, and dissenting in part, post, p. 922. REHNQUIST, C. J., filed an opinion concurring in the judgment in part and dissenting in part, in which WHITE, SCALIA, and THOMAS, JJ., joined, post, p. 944. SCALIA, J., filed an opinion concurring in the judgment in part and dissenting in part, in which REHNQUIST, C. J., and WHITE and THOMAS, JJ., joined, post, p. 979.
Assuming I've understood correctly, that's 7 opinions filed. However, you could argue there's only 4 distinct lines of thought with Rehnquist-White-Scalia-Thomas all agreeing, O'Connor-Kennedy-Souter all agreeing and Blackmun and Stevens doing their own thing. Additionally you could consider it 5 if you're counting distinct written opinions but not counting Blackmun and Stevens's separate partial joining with O'Connor-Kennedy-Souter as distinct opinions.