Car ID Help

This is a picture of my great-grandmother sitting in an unknown race car of sorts.  I have done lots of work, but established little.  It appears to be a handmade racer, judging by the fact that it has BMW front fenders, but a strange grille and no badges.  The grille seems to have been cut out from metal, again seemingly handmade.  I can tell you that the license plate is a New York plate, dated 1924.  I'd appreciate it if anybody could tell me anything more about this car.
Thanks.