The phrase "after some conversations" is correct and usable in written English.
It can be used to indicate that a conclusion or decision was reached following a series of discussions or dialogues.
Example: "After some conversations with the team, we decided to move forward with the project."
Alternatives: "following several discussions" or "after a few talks".
The events had been planned as shows of support for Obamacare, but, after some conversations, they were billed as a Unity Tour, to demonstrate that the Party had healed.
He and his modest entourage turned up at the top of the lower grandstand behind home plate, and, after some conversations there, he was announced as he slowly came down the aisle and took a seat a few rows above the box-seat sector.
But after some conversations with Rose, they figured out "a win for both of us.
And after some conversations with the team, Loenngren ended up quitting his job and relocating to New York where the idea for Convies soon came about.
"After some conversations she very quickly came around".
After some conversations at bars on U Street and the Hill turned south when his Trump ties came up, one since-departed staffer has learned to reveal his White House past only as a last resort.
After some conversation, a police officer was dispatched, and he called for backup.
After some conversation, she finally says: "Tell me about the closest person in your life who you're comfortable talking about.
After some conversation about how the protesters had been faring in Zuccotti Park, Mr. Black pointed to a group of people marching along the sidewalk toward Foley Square.
After some conversation with producers he decided to go to a hospital, and NBC, which said he probably had a stomach virus, showed a repeat on Thursday night.
There, after some conversation, the customer said that he had been hired by Maria Konstan to kill Berkovits but, having found his assigned target to be a decent man, had decided that he couldn't go through with it.
