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Segment Information - Schedule of Total Revenues, Segment Operating Profit and Total Asset for Reporting Segment (Details) - USD ($)
$ in Thousands
 3 Months Ended 9 Months Ended
Jun. 30, 2023
Jul. 01, 2022
Jun. 30, 2023
Jul. 01, 2022
Segment Reporting Information [Line Items]        
Revenues $ 4,186,702 $ 3,827,093 $ 12,063,702 $ 11,041,777
Total Segment Operating Profit 269,741 265,762 797,408 609,310
Restructuring, Transaction and Other Charges (35,245) (10,150) (94,742) (210,986)
Total Other Expense, net (43,056) 6,353 (120,930) (12,825)
Earnings from Continuing Operations Before Taxes 226,685 272,115 676,478 596,485
Amortization of intangible assets     152,232  
Cost incurred in investment 17,200   17,200  
Spin off charges     39,088  
Real estate related impairments and other transformation     38,100 74,600
Final pre-tax settlement   91,300   91,300
Gain related to cost-method Investments   13,900    
Gain on termination of lease     900 7,100
Spinoff        
Segment Reporting Information [Line Items]        
Spin off charges 13,400   13,400  
AWE Management Ltd        
Segment Reporting Information [Line Items]        
Investment income associated with final exit activities       3,500
Operating Segments        
Segment Reporting Information [Line Items]        
Total Segment Operating Profit 423,472 365,799 1,211,946 1,104,775
Corporate        
Segment Reporting Information [Line Items]        
Other Corporate Expenses (118,486) (89,887) (319,796) (284,479)
Corporate | Other Expense        
Segment Reporting Information [Line Items]        
Amortization of intangible assets 52,000 51,600 152,200 146,900
One-time benefit program changes     15,000  
Changes in employee benefit programs 41,000      
Company technology platforms and other personnel and corporate overhead cost increases 26,000      
Critical Mission Solutions | Operating Segments        
Segment Reporting Information [Line Items]        
Revenues 1,190,845 1,109,034 3,457,076 3,220,193
Total Segment Operating Profit 99,141 88,328 275,304 274,184
People & Places Solutions | Operating Segments        
Segment Reporting Information [Line Items]        
Revenues 2,469,694 2,222,530 7,041,744 6,306,520
Total Segment Operating Profit 242,673 213,930 701,498 595,485
Divergent Solutions | Operating Segments        
Segment Reporting Information [Line Items]        
Revenues 239,289 217,949 694,978 650,120
Total Segment Operating Profit 20,794 12,093 57,623 52,256
PA Consulting | Operating Segments        
Segment Reporting Information [Line Items]        
Revenues 286,874 277,580 869,904 864,944
Total Segment Operating Profit $ 60,864 $ 51,448 $ 177,521 $ 182,850