https://www.gnu.org/software/gawk/manual/html_node/Arrays-of-Arrays.html

X[a,b]

split(X,x_bits,SUBSEP);

   Arrays
       Arrays  are  subscripted  with an expression between square brackets ([ and ]).  If the expression is an expression list (expr, expr ...)  then the array subscript is a string con‐
       sisting of the concatenation of the (string) value of each expression, separated by the value of the SUBSEP variable.  This  facility  is  used  to  simulate  multiply  dimensioned
       arrays.  For example:

              i = "A"; j = "B"; k = "C"
              x[i, j, k] = "hello, world\n"

       assigns the string "hello, world\n" to the element of the array x which is indexed by the string "A\034B\034C".  All arrays in AWK are associative, i.e., indexed by string values.

       The special operator in may be used to test if an array has an index consisting of a particular value:

              if (val in array)
                   print array[val]

       If the array has multiple subscripts, use (i, j) in array.

       The in construct may also be used in a for loop to iterate over all the elements of an array.  However, the (i, j) in array construct only works in tests, not in for loops.

       An  element  may be deleted from an array using the delete statement.  The delete statement may also be used to delete the entire contents of an array, just by specifying the array
       name without a subscript.

       gawk supports true multidimensional arrays. It does not require that such arrays be ``rectangular'' as in C or C++.  For example:

              a[1] = 5
              a[2][1] = 6
              a[2][2] = 7

       NOTE: You may need to tell gawk that an array element is really a subarray in order to use it where gawk expects an array (such as in the second argument to split()).  You  can  do
       this by creating an element in the subarray and then deleting it with the delete statement.

$ awk -V
GNU Awk 4.1.4, API: 1.1 (GNU MPFR 3.1.5, GNU MP 6.1.2)

BEGIN {
        Z[1]["Jim"]["The quick brown fox jumps over the lazy dogs"]=42;
        Z[1]["Harry"]["Colorless green ideas sleep furiously"]=41;
        Z[2]["Jack"]["The quick brown foxes jumps over the lazy dogs"]=40;
        Z[2]["Harry"]["Colorless green ideas sleep furiously"]=39;
        Z[3]["Joe"]["The quick brown foxes jumps over the lazy dog"]=38;
        Z[4]["James"]["The quick brown fox jumps over a lazy dog"]=37;
        Z[5]["Jimmy"]["The quick brown fox jumps over the lazy dog again"]=36;
      }
END {
print "Z[a,b,c]";
for ( a in Z )
        for ( b in Z[a] )
                for ( c in Z[a][b] )
                        print "a of Z[a]: " a "\t| b of Z[a][b] :\t" b  "\t| c of Z[a][b][c]:\t" c " |\t\tvalue of Z[a][b][c]:\t" Z[a][b][c];
}

$ awk -f demo.awk </dev/null
Z[a,b,c]
a of Z[a]: 1	| b of Z[a][b] :	Harry	| c of Z[a][b][c]:	Colorless green ideas sleep furiously |		value of Z[a][b][c]:	41
a of Z[a]: 1	| b of Z[a][b] :	Jim	| c of Z[a][b][c]:	The quick brown fox jumps over the lazy dogs |		value of Z[a][b][c]:	42
a of Z[a]: 2	| b of Z[a][b] :	Harry	| c of Z[a][b][c]:	Colorless green ideas sleep furiously |		value of Z[a][b][c]:	39
a of Z[a]: 2	| b of Z[a][b] :	Jack	| c of Z[a][b][c]:	The quick brown foxes jumps over the lazy dogs |		value of Z[a][b][c]:	40
a of Z[a]: 3	| b of Z[a][b] :	Joe	| c of Z[a][b][c]:	The quick brown foxes jumps over the lazy dog |		value of Z[a][b][c]:	38
a of Z[a]: 4	| b of Z[a][b] :	James	| c of Z[a][b][c]:	The quick brown fox jumps over a lazy dog |		value of Z[a][b][c]:	37
a of Z[a]: 5	| b of Z[a][b] :	Jimmy	| c of Z[a][b][c]:	The quick brown fox jumps over the lazy dog again |		value of Z[a][b][c]:	36