No need to make up new operatorsadd a method to every single class when a sub will do just fine.

sub cando {
   my $o = shift;
   my $m = shift;
   return if !eval { $o->can($m) };
   return $o->$m(@_);
}

my $home =  cando($self, 'home')
         // cando($self, 'house', 1)
         // confess(q{Can't determine home});
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Keep in mind neither your operatormethod nor this sub will work right if home returns undef.