I'm not entirely sure I understand the precise behavior that the OP would like to see, but perhaps something like this is closer to what they have in mind:

package MyObj;
use Class::MakeMethods::Autoload { 
  'new' => 'Template::Hash::new', 
  '.*'  => 'Template::Inheritable::code_or_scalar -method',
};
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The usage is only slightly different from Class::SelfMethod:

my $person = MyObj->new();

# Simple string get/set
$person->name("Smith");
print $person->name();

# Define a method on the class so all instances will share it
MyObj->greeting( sub { "Hello, " . (shift)->name } );
print $person->greeting();

# Override the method for a particular instance
$person->greeting( sub { "Hi " . (shift)->name } );
print $person->greeting();

# You can change the method repeatedly with the same syntax:
$person->greeting( sub { "Hi there!" } );
print $person->greeting();
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If you want a different interface, you may be able to specify it by changing the parameters passed to Class::MakeMethods::Autoload.