Could an annual plant be genetically modified to be a perennial?
Researchers at Ghent University have made a discovery that downregulation of the proteins CONSTANS 1 (SOC1) and FRUITFULL (FUL) lead to the development of many perennial traits in annual plants (in the study Arabidopsis thaliana is used) (reference). 

The CONSTANS gene controls flowering in Arabidopsis thaliana (reference). 

FRUITFULL (FUL) is an MADS box gene that functions early in controlling flowering time, meristem identity and cauline leaf morphology and later in carpel and fruit development in Arabidopsis thaliana (reference).

The process is complicated and would need many genes to be manipulated but this research proves that it is possible. Another article of interest.