Generally, private process service fees are considered costs that may be recoverable. However, I cannot answer with specificity regarding your particular jurisdiction.
You'll want to be careful in accepting generalities without specificity. In legal matters, that can lead to both specific and general problems, including, but not limited to, specific legal problems for which you may be liable.
For instance, under Wisconsin statutes, with regard to garnishment actions, one who improperly files such and action may be fined by the Court - something you'll likley want to avoid.
If you are considering filing for garnishment, you'll also want to ensure that you are using the proper terms, as well as the proper form of pleadings.
Check out Wis. Stats. section 812.44(2) for the proper form for garnishment of earnings, or wages (link here: http://www.legis.state.wi.us/statutes/Stat0812.pdf scroll down to pages 7 & 8)
In the statutorily required form, there is a blank for entering "Costs of this earnings garnishment" this is where you would include those costs in an action for earnings garnishment.
As with any legal matter, a thorough review of your facts and circumstances by an expereinced attorney is recommended. Note this answer provides general information only with regard to unconfirmed and unknown facts and circumstances and does not constitute legal advice with regard to any specific matter, nor does an attorney client relationship exist herein.
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