The phrase "after several exchanges" is correct and usable in written English.
You can use it to indicate that multiple communications or interactions have taken place before a certain point or conclusion.
Example: "After several exchanges, we finally reached an agreement on the terms of the contract."
Alternatives: "following multiple discussions" or "after numerous conversations".
After several exchanges, mainly with Orazio Grassi (1583 1654), a professor of mathematics at the Collegio Romano, he finally entered the argument under his own name.
After several exchanges over the deletions he was dismissed for what the museum called "just cause" — which means that it did not offer him severance pay — on June 11.
After several exchanges, one author joined my thesis committee and I added a new specific aim to my thesis.
After several exchanges with me, Google has agreed to propose solutions in the four specific areas of concern that we have identified.
After several exchanges, EPA concluded in March 2014 that the agency had complied as fully as it was able to with the requests for data.
After several exchanges, Sebelius named Michelle Synder, the chief operating officer for the Centers for Medicare & Medicaid Services.
Although at first nonplussed, after several similar exchanges Lucy eventually did as asked.
Science's editors, however, disagreed after they had looked into the matter.In 2005, after several bitter exchanges, Dr Fang managed to identify the Confused Professor as Dr Xiao.
As in the 'Tom Cruz' movie 'Gerry maguire' a quote from 'Actor Cuba Gooding' an athlete Cruz was representing said to 'Cruz' (a famous Quote) 'Show Me the Money.' " After several more exchanges, Mars decided that it was e-mails like these which had scared off potential buyers.
There are three recognized phases in a chess game: the opening, where piece development and control of the centre predominate; the middlegame, where maneuvering in defense and attack against the opponent's king or weaknesses occurs; and the endgame, where, generally after several piece exchanges, pawn promotion becomes the dominant theme.
The attorney general reportedly offered to step down after several "heated" exchanges with the president. .
