Based on the USA PATRIOT Act, one action that the US might take to demonstrate extraterritorial reach is to send requests for information to a non-US based financial institution (FI). The USA PATRIOT Act expanded the authority of the US government to issue subpoenas and other legal orders to foreign banks that maintain a correspondent account in the US, requiring them to produce records relating to such account or any account at the foreign bank, including records maintained outside the US12. This provision was intended to enhance the ability of the US to investigate and prosecute money laundering and terrorist financing activities that involve foreign FIs3.
Reference:
1: USA PATRIOT Act, Section 319(b)
2: Britannica, USA PATRIOT Act, History & Society
3: Princeton Legal Journal, FISA and the USA PATRIOT Act: Reforms and Legal Implications