I don't know much about the inner workings of modules & loading/unloading, but this appears to work:
This is X1.pm:

package X;
sub new {
  my $self = shift;
  printf "new() v1\n";
  return bless {}, $self;
}
sub blah {  printf "blah v1\n"; }
1;
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This is X2.pm:

package X;
sub new {
  my $self = shift;
  printf "new() v2\n";
  return bless {}, $self;
}
sub blah {  printf "blah v2\n"; }
1;
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This is the test script, x.pl:

#!/usr/bin/perl
use lib '.';
use X;
my $x1 = X->new();
$x1->blah;
printf "Copying in X2.pm\n";
system("cp X2.pm X.pm");
printf "Trying X.pm\n";
eval `cat X.pm`;
$x1->blah;
my $x2 = X->new();
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And this is the execution and output:

[me@host tmp]$ cp X1.pm X.pm
[me@host tmp]$ ./x.pl
new() v1
blah v1
Copying in X2.pm
Trying X.pm
blah v2
new() v2
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While it didn't work for we to just 'use' or 'require' the modules again (i didn't really except it to, especially 'use' since that's done early on), it appears to work to eval in the new module. Is this a good or a horrible implementation/usage? I really can't say--hopefully someone wiser will comment...