Rather than clients keeping a reference to the object, you might use something more akin to the Singleton pattern instead. E.g. something along the lines of Foo->current_instance() that you either use every time you need it or keep in a lexical for (say) the scope of a single sub call.

sub do_bar {
  my( $a, $b ) = @_;
  my $cur_foo = Foo->current_instance;
  ##
  ## Use $cur_foo . . .
  ##
  return $zorch;
}
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So each time it's used you'll have the "current" Foo. If you need to change the current instance your private code calls something like Foo->_set_instance( $new_foo ) behind the scenes.