Can a protest be filed after a patent application has been published?

Yes, but with restrictions. According to MPEP 1901.06:

“35 U.S.C. 122(c) permits the filing of a protest in an application after the application has been published if there is express written consent of the applicant.“

To file a protest after publication, the following conditions must be met:

• The protest must be accompanied by the written consent of the applicant.
• It must be filed prior to the date the notice of allowance is given or mailed.
• The protest must comply with the requirements of 37 CFR 1.291(b) and (c).

The applicant’s written consent can be specific to a particular protest or can be a blanket consent for certain types of protests.

Examiner Must Conduct Normal Examination Despite Protest MPEP 1901.06 Required
Office Reviews Protests Before Recording MPEP 1901.06 Informative
Reissue Application Related to Pending Interference Must Be Referred MPEP 1901.06 Recommended
Minor Compliance Errors Allow Protest Entry MPEP 1901.06 Permitted
Protest With Minor Errors Can Be Entered MPEP 1901.06 Permitted