Or, just to keep it simple, and more like what was requested originally (as there may be something else that we don't know about, that would have problems if it were a deep structure), you can use a flat hash:

my %data;
$data{'exampleother1'} = 'something';
$data{'exampleother2'} = 'something else';
$data{$var1.$var2.$number} = $value;

# or using a hashref
my $data;
$data->{'exampleother1'} = 'something';
$data->{'exampleother2'} = 'something else';
$data->{$var1.$var2.$number} = $value;
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The deeper structure has advantages if you might have values for ($var1.$var2) that collide. (if those should be two discrete values, then use a hash of hashes or some other complex structure. If they should be the same value, then just use a single dimensional hash).