It looks very much like you intent SomeClass to be a sublcass of SomeOtherClass. Why does it look this way? Because you assume that both classes have $self->{cgi} hold an instance of CGI, you show it being set up in SomeClass, but not in SomeOtherClass.

If you change SomeClass to read

  package SomeClass;
  use base qw(SomeOtherClass);
  ...
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then you can write

  sub run {
      my $self = shift;
      $self->SomeSub();
  }
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Doing this does not create a new instance of the CGI module. Methods (subroutines) from both SomeClass and SomeOtherClass both have access to the same instance of CGI.