You can share references, just not in quite the same way. Instead of my $ref : shared = {};, use my $ref = &share({});. To share a multidimensional object you will also need to share the anonymous refs in your code the same way, so for your second example you will have to do:

use threads::shared;
my $ref = &share({});
$ref->{a} = &share([]);
$ref->{a}[0] = something;
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For shared objects you can use the same technique: my $ref = &share(someobj::new()). (Note that this is covered in the threads::shared documentation).