I'd write a separate method to add thingies:

package Wibble;
use Moose;

has 'thingies' => (is => 'rw', isa => 'ArrayRef' default => sub { [] }
+);

sub add_thingies {
    my $self =  shift;
    push @{ $self->thingies }, ref $_ ? @$_ : $_
      for @_;
}

package main;

my $w = Wibble->new( thingies => [ 'this', 'that' ] );
print join( ", ", @{ $w->thingies() } ) . "\n"; # this, that
$w->add_thingies('another');
print join( ", ", @{ $w->thingies() } ) . "\n"; # this, that, another
$w->add_thingies('and', [qw/some more/]);
print join( ", ", @{ $w->thingies() } ) . "\n"; # this, that, another,
+ and, some, more
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