Can a plane with 2 sets of shorter wings fly?
What you are proposing is called a "tandem wing", and it's been done before. A brief search should produce more than enough research papers about the advantages and disadvantages of this particular design.

The near-complete absence of multiple-wing designs in modern aviation should be a hint that the design has issues. Unless you particularly need the advantages of the design more than the drawbacks, there's no particular reason to use it.