Using Baseball Reference's Play Index, I looked for games with the most number of players who started and finished the game and had exactly one hit. (Obviously, the highest number would be nine (whether having the pitcher hit or using a DH).)
I found 17 games since 1908 (the earliest year for which we have fully searchable box scores).
Giants vs Phillies October 1, 1908 (G1) Boston (NL) vs Phillies July 3, 1909 (G2) Senators vs Red Sox Septmeber 13, 1911 Cleveland vs Tigers July 4, 1916 (G2) Phillies vs Cubs May 21, 1917 Pirates vs Reds May 27, 1921 Reds vs Cubs May 30, 1924 (G2) Athletics vs White Sox September 27, 1928 Red Sox vs Browns July 14, 1940 (G2) Cleveland vs Browns May 31, 1948 (G1) Rangers vs Twins August 6, 1976 Athletics vs Angels July 28, 1977 Blue Jays vs Athletics July 1, 1990 Orioles vs Royals July 11, 1990 Angels vs Orioles May 23, 1992 Tigers vs Twins June 14, 1996 Rangers vs Athletics May 3, 2008However, the Phillies pitcher did not finish Tuesday's game. So I then looked for games with the most number of players who started the game and had exactly one hit. There were 77 of those games before the Phillies joined the list. It has happened way more often than I would have thought.
Thanks to Jeff A. for alerting me to the Phillies' box score. (This certainly falls under my love of unique linescores.)
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Bonus: What is the most hits a team has had when no player had more than one hit?
Answer: 12.
Mets vs Cubs on September 18, 1977 (G2) (13 players batted)
White Sox (vs A's), September 7, 1970 (G2) (16 players batted)
(It's a little strange that both instances were the second games of doubleheaders.)
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