People gather near BYD's new electric cars at the Beijing International Automotive Exhibition last month. | REUTERS

BEIJING – China's carmakers are hunting for their own "Yaris moment" — the ⁠kind of locally tailored breakthrough that helped Toyota conquer Europe — as they race to turn booming exports into lasting overseas growth.

After early attempts that largely involved exporting China-designed cars with minor tweaks, automakers are now re-engineering vehicles from the ground up for foreign buyers, driven as much by fierce margin pressure at home as by opportunity abroad.

China's overcrowded domestic market has been locked in a bruising price war for years, leaving many manufacturers struggling to make money.…