You have:

`$swlist -l depot @ $depot_locn | $grep $rel_string | $grep $i | $grep
+ AR >> blah`
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which isn't pure perl code anyway, is it? (It's convenient to call grep 3 times, but might be more efficient to do with Perl's own grep.) Here, you're using perl just like you would use sh.

But to address your question, try:

`$swlist -l depot @ $depot_locn | $grep $rel_string | $grep $i | $grep
+ AR | tee file1 | tee file2 | tee file3 >> tee file4`
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But if you need append, I don't think tee can do that.

Also take a look at Regexp Quote Like Operators and What's wrong with using backticks in a void context?