The phrase "alternated among" is correct and usable in written English.
It can be used when describing a situation where multiple items or subjects are switched or rotated between a group.
Example: "The colors of the flags alternated among red, white, and blue throughout the parade."
Alternatives: "switched between" or "rotated among".
As their well-wishers gathered to leave, the couple alternated among handshakes, hugs and customary bows.
A year later Mr. Newman was switched to tenor; thereafter he alternated among tenor, baritone and alto, recording solos on all three.
The Syrians would replace Bangladesh in a seat that is alternated among nations in the General Assembly's Asian regional bloc, which includes the Middle East.
Yet Mr. Biddle handled the Reynolds case with punctilious diligence and honor, while his adversaries alternated among lawyerly evasions, outright lies and unseemly bullying.
During the following centuries, rule alternated among Venice, Genoa, and the Turks, who after 1670 used it as a place for banishment of exiles.
This creative assignment was met with cheers, giggling, and hesitant questioning: "Do we really have to do this?" "But I can't draw". While working the students alternated among hilarity, focused examination of the text, and serious theoretical discussion.
We find that as overlapping genes become longer, they have a tendency to alternate among alternative overlap phases.
Parasites have evolved by three major evolutionary routes to alternate among two or more hosts.
Mr. Geers tapped the screen with a stylus to alternate among images.
Chapters alternate among four main characters and are short enough to leave you wanting more.
The novel follows the members of a New Orleans family immediately after Hurricane Katrina, alternating among their perspectives.
