I think the concept that you are looking for is 'Object inheritance'. (the exact term, to tell a scalar what package it belongs to is bless

my $local1 = my_module->new();
$local1->func1();
$local1->func2();

my $local2 = my_module->new();
$local2->func1();
$local2->func2();

package my_module;
use base qw(a_module);
sub func1 { shift->do_something1() }
sub func2 { shift->do_something2() }
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This will work so long as a_module is set up correctly for inheritance. If it isn't (you can tell because ref($local1) will be 'a_module' and not 'my_module'), it'll behave the same way you've been having problems with, and you'll need to add within your package:

sub new {
    my $class = shift;
    return bless a_module->new(), ref($class) || $class;
}
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