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Phrase(s): push ahead (with something)
1. Lit. to go on ahead, pushing with something. • The worker pushed ahead with the plow, moving the snow to the side of the road. • Our car followed the snowplow, which was pushing ahead at a fast clip. 2. and push ahead (on something) Fig. to continue to progress with something. • Let’s push ahead with this project immediately. • I want to push ahead on this project.
McGrawhill's American Idioms And Phrasal Verbs