The most infamous such attempt was that of the young, engineering-savvy Chrysler Corporation. It introduced a line of cars with advanced engineering features and an unusual appearance resulting from aerodynamic testing in wind tunnels. By "unusual," I'm referring to how different the cars looked when compared to cars potential buyers were seeing on streets and highways. Early 30s cars were rather square, boxy-looking affairs with distinctly separate fenders, headlamps, spare tires and other bits. True, this was being softened as valances were added to fenders and windshields and grilles were tilted back slightly as hints of attention being paid to reducing wind resistance.
This is covered in more detail with regard to the Airflow here. As it happened, the Airflow was not a sales success, though its layout of the drivetrain and passenger compartment quickly influenced the rest of the industry. Some blame the sales failure on production delays and criticisms planted by competitors, but it's hard to deny that styling was a good part of the problem. The 1934 Airflows had rounded, stubby-looking hoods and grilles that contrasted sharply with the high, long hoods on competing cars. So a crash facelift was put into place for 1935. The most cost-effective solution was to raise the hood and attach a more conventional grille.
Despite its market problems, the Airflow was inspirational to three carmakers in other countries. Sales success of these cars is hard to evaluate. For instance, the Toyota AA was Toyota's first car, so there can be no comparison to previous sales. Sweden's Volvo was an existing car maker, but its 1935-38 PV 36 Carioca didn't sell very well, in part due to its high price. On the other hand, The French Peugeot 402 was successful enough that a smaller, very similar 202 series was introduced a few years later.
This is the original Airflow shown in a publicity photo with the radical-at-the-time Union Pacific M-10000 streamlined train.
The rear of the car hadn't changed much in two years, but the hood and grille were redesigned for 1935 and further facelifted in 1936.
There was a DeSoto Airflow line introduced in 1934 along with Chrysler's. The DeSotos had a shorter wheelbase, the appearance difference having to do with the distance between the dash cowling and the front axle line, as can be seen in this car auction photo. There too was a 1935 facelift focusing on the hood and grille, but the 1936 DeSoto Airflows had only detail changes in the grille for 1936 because the line ceased after that year. Chrysler Airflow production continued through 1937.
Production versions for 1936 were the same as the car pictured here. Unlike Chrysler and DeSoto four-door sedans, the Carioca was a four-window instead of a six-window style. Airflow similarities are many, including the rear fender skirt treatment and the positioning of the headlamps.
Toyota didn't place the headlights in the body, instead having them freestanding, a practice still common in 1936. The AA was a six-window affair and the sheet metal shaping on the front is very Airflow-like. One missing item seems to be rear fender skirts.
The 402 model Peugeot debuted for the 1936 model year and was little changed in 1939. The hood/grille treatment is more in line with the original 1934 Airflows, but there is no "cheek" panel on either side of the grille, as seen in all the cars shown above. Headlamps were placed behind the grille bars, a feature unique to Peugeot. Perhaps most important is that the 402 has a sleeker appearance than the others.