How can I travel overseas while waiting for my EB-5 biometrics appointment for my I-485?

Unfortunately, while an adjustment of status application is pending, one cannot travel internationally until a travel authorization is issued. Should a departure occur before the travel document is issued, the adjustment of status application may be deemed abandoned.

He may only travel on the valid visa or must await the travel document. Urgent requests can be tried only due to an emergency such as health matter and documentation would be required.

If there is an emergency family or business reason, you can apply for an expedite on the advance parole document.

If he has a valid H or L visa, he can depart the United States without abandoning his I-485 application. Otherwise, he must wait until he receives the advance parole travel document. If a humanitarian situation exists, he can request the USCIS to expedite the travel document, but this usually requires a deceased or dying close family member. Aging parents usually do not constitute an urgent humanitarian situation unfortunately.

You can apply for an emergency advance parole at the local office. Call USCIS nd ask for an INFOPASS and say you need an emergency travel permit with I-485 pending.

You may be able to make an Infopass appointment at your local USCIS field office, but the Trump administration made that very difficult to do and the COVID closures did not help. Still, a call to USCIS may work.

Whether he can go depends on whether he can get expedited I-751. Should he have proof for emergency needs, he can go to USCIS office to request emergency travel document.

If there is an actual emergency requiring international travel, he could consider seeking an emergency appointment for AP. These are not easy to get now and it also depends where in the U.S. you are.