The phrase "already preoccupy" is not correct in written English.
The word "preoccupy" already implies a sense of being occupied or engaged with something, so "already" is redundant.
Example: "I find myself preoccupied with thoughts of the upcoming project."
Alternatives: "currently occupy" or "already engage."
"The government is already preoccupied by domestic issues".
Since the Justice Department was already preoccupied with the Microsoft case, the commission took the Intel case.
But at the time, he was already preoccupied with the subject of financial risk.
The music Van der Graaf Generator made as young men was already preoccupied with destruction and impermanence.
Why do you burden us with this when we are already preoccupied with Mini-Den, Edith's pregnancy and the deathly pallor in Cousin Violet's face?
Since Musk is already preoccupied with his other projects, such as SpaceX and Tesla, he has made plans for Hyperloop open to the public allowing other entrepreneurs to make it a reality.
He was already preoccupied with thoughts of Game 5, which Oakland must play without its cleanup hitter, Jermaine Dye, who fractured his left leg when he fouled a ball off it in the third inning today.
Already preoccupied with mathematics, he gets off before it crosses a bridge that he is unconvinced can bear the load; the train plunges into the monsoon-swollen river below.
Prospects for legislation had dimmed as lawmakers, already preoccupied with legislation on homeland security and Iraq, prepared to leave town soon for the final weeks of the campaign season.
It meant the country was already preoccupied by the in-custody death of a young African American man when Rankin took that early-morning 911 call and confronted 18-year-old William Chapman in the Walmart's vast car park.
