There are new details on American Airlines' expanding partnership with Taiwanese carrier Starlux.

On Tuesday, we reported that the airlines had signed a new agreement that would allow them to codeshare on flights, potentially opening the door to an even bigger alliance in the future. On Wednesday, the news got even better, with word that a frequent flyer partnership is also happening. You can now earn American Airlines miles and Loyalty Points on select Starlux flights.

American Airlines confirmed the news to TPG: "AAdvantage® members purchasing a codeshare flight under the partnership can earn miles and Loyalty Points."

The airlines are also working to allow mileage redemption on each other's flights.

We've also learned that those codeshares include one of Starlux's newest routes — from Taiwan Taoyuan International Airport (TPE) to Phoenix Sky Harbor International Airport (PHX) — pending regulatory approval.

Flights are available to book now for travel starting Sept. 30.

"Taipei remains a top destination for global business, visiting friends and family and leisure travel and together with Starlux Airlines, we're partnering to provide new travel options," said American's senior vice president of alliances, Anmol Bhargava. "We look forward to working with Starlux on opportunities to make the journey even more rewarding for customers."

American Airlines already had an interline agreement with the startup airline, allowing passengers to book travel involving both airlines and check their bags through to their final destination. Now, the airlines will also start codesharing on some flights as of Sept. 30.