Both and

Point 17 in CONJUNCTIONS coordinating is defined as:

‘BOTH AND’ to combine phrases and clauses, often for emphasis.

In the iWeb corpus we can run up to 4 wildcards with different combinations:
'both * * and * *'

 

1 BOTH MEN AND WOMEN 28482
2 BOTH ON AND OFF 13750
3 BOTH YOU AND YOUR 13393
4 BOTH INSIDE AND OUTSIDE 11752

5 BOTH MALE AND FEMALE 9349 (most common collocate: ‘organs’)

6 BOTH PUBLIC AND PRIVATE 7792
7 BOTH BEFORE AND AFTER 7613
8 BOTH INTERNAL AND EXTERNAL 7538
9 BOTH GOOD AND BAD 7273
10 BOTH POSITIVE AND NEGATIVE 7086

1 BOTH THE PUBLIC AND PRIVATE SECTORS 2108
2 BOTH AT HOME AND ABROAD . 1448
3 BOTH A BLESSING AND A CURSE 1419
4 BOTH MEN ‘S AND WOMEN ‘S 1059
5 BOTH THE PRIVATE AND PUBLIC SECTORS 973
6 BOTH THE GOOD AND THE BAD 763
7 BOTH THE HOUSE AND THE SENATE 753
8 BOTH THE PUBLIC AND PRIVATE SECTOR 729
9 BOTH THE FRONT AND BACK OF 717
10 BOTH THE OLD AND NEW TESTAMENTS 717

1 BOTH THE MEN ‘S AND WOMEN 1388

2 BOTH IN THE UK AND INTERNATIONALLY 576

3 BOTH IN THE UK AND ABROAD 569
4 BOTH IN THE UK AND OVERSEAS 533
5 BOTH THE UNITED STATES AND CANADA 517
6 BOTH THE UNITED STATES AND THE 473
7 BOTH IN THE U.S. AND ABROAD 416
8 BOTH IN FRONT OF AND BEHIND 409
9 BOTH AS DECIMAL FRACTION AND IN 371
10 BOTH IN THE CLASSROOM AND IN 361

1 BOTH IN THE UNITED STATES AND 1620
2 BOTH MEN AND WOMEN , AND 646
3 BOTH THE HOUSE OF REPRESENTATIVES AND 259
4 BOTH IN TERMS OF TIME AND 207
5 BOTH SIDES OF THE ATLANTIC AND 206
6 BOTH IN THE SHORT TERM AND 201
7 BOTH SIDES OF THE BALL AND 201
8 BOTH AT THE SAME TIME AND 197
9 BOTH HERE IN THE UK AND 194
10 BOTH PHYSICALLY AND MENTALLY , AND 155