You can add New Japan to his itinerary.
The blade-wielding Moxley was revealed to be the subject of New Japan's "Time's Up" video, with June 5, 2019 (the day for the Best of the Super Juniors finals) specifically mentioned.
Moxley, who certainly enjoys social media more than Ambrose did, tweeted out a vignette (tagging New Japan's handle) that depicts IWGP United States champion Juice Robinson as his next target.
AEW President Tony Khan did mention late Saturday that Moxley is full-time with the company, but only after the TV show premieres this fall. Moxley is, per his contract, free to take international dates when his schedule is light, such as now, when AEW is only running sporadically.