Thrice doesn’t really fit the sentiment of the sentence there. It would be best to replace “both” with nothing in that sentence when moving from two to three it

Thrice doesn’t really fit the sentiment of the sentence there. It would be best to replace “both” with nothing in that sentence when moving from two to three items. “Both” itself isn’t necessary when dealing with two items (not that it hurts, IMO). It could serve a rhetorical purpose if you particularly wanted to emphasize the equal relationship between the two items. E.g., if one item might normally be perceived as significantly more important than the other, “both” is a way to address the surprise or skepticism the reader may feel seeing them placed together equally.