All "BUILD" methods in the inheritance chain will be called, so subclasses need not know about parents:

class Dot {
    has $.x;
    has $.y;
    has $!z;

    submethod BUILD(:$!x, :$!y, :$!z) {
        say "Initializing!";
    }

    method get {
        return ($!x, $!y, $!z);
    }

    method getz {
        return $!z;
    }
}

class Dot2 is Dot {
    has $!w;

    submethod BUILD(:$!w) {
        say "Initializing 2!";
    }

    method get {
        # No access to $!z here of course (it is private)
        # Also note use of public $.x, $.y not private $!x, $!y
        return ($.x, $.y, $!w);
    }
}

my $a = Dot2.new(x => 23, y => 42, z => 2, w => 12);
say $a.get;
say $a.getz;
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