It may be a little overkill, but my MZMT shipping module will do this for you.
You'd setup your table using the count method to be "0:100%" (which translates to $1 per item [100% of the number of items])
Then, depending on what you want ($3 for 1 item, $4 for 2 items, $5 for 3 items, etc... --or-- $4 for 1 item, $5 for 2 items, $6 for 3 items, etc...), you would set the handling fee for the table to be either $2 or $3
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