Archibald has added three new faces to his squad so far this summer, including former Coventry City defender Dan Seaborne.
However, Partick's boss hopes to boost his ranks even further ahead of transfer deadline day on September 1.
"We definitely need another couple in. We are short in a few areas and it's something we are working on all the time," he is quoted as saying by Sky Sports News.
"We probably need one more for the striker area and at full-back. We are in talks with a number of players."
Partick continue their Scottish Premiership campaign on Wednesday at home to Ross County.