use strict;

my $filename = "file.name"; # or whatever

my $obj_count = 0;
open( FILE, "<", $filename ) or die "$filename: $!\n";
while (<FILE>) {
    $obj_count++ if /^SS/;
}
close FILE;

my $part_count = get_some_number();  # depends on ... (command line? DB?)
my $obj_per_part = $obj_count / $part_count;
my $break_at_obj = $obj_per_part;

open( FILE, "<", $filename );

my $o_index = sprintf( "%03d", 1 );
open( OUT, ">", "$filename.$o_index" ) or die "$filename.$o_index: $!\n";
my $obj_done = 0;

while (<FILE>) {
    if ( /^SS/ ) {
        if ( $obj_done > $break_at_obj ) {
            close OUT;
            $o_index++;
            open( OUT, ">", "$filename.$o_index" ) or die "$filename.$o_index: $!\n";
            $break_at_obj += $obj_per_part;
        }
        $obj_done++;
    }
    print OUT;
}