Yes—you can absolutely apply for and receive a second U.S. passport, thereby having two passports with concurrent validity, which can be used interchangeably. The passport is issued as a courtesy at the discretion of the State Department, but applications are regularly approved—the period of validity for your second passport will be two years, nonrenewable. The State Department will issue you a second passport if you can demonstrate a need for the document. Per the State Department website, acceptable reasoning in support of your application includes:A foreign country will deny a visa or entry to the bearer of a passport containing markings or visas showing travel to certain other countries;A passport needed for immediate travel is unavailable due to delays in processing a foreign visa application, or if the applicant has the need to obtain multiple visas on a current or ongoing basis, e.g., flight personnel for international airlines, executives of multi-national companies, or international journalists.(sources various: Apply for a Second Passport | U.S. Embassy & Consulates in Germany, Apply for a Second Regular Passport | U.S. Embassy & Consulates in France)Your request would obviously fall under the first category. In order to request a second passport, you’ll need to fill out a either a DS-11 or DS-82 passport renewal form, and include a photo which meets State Department passport photo requirements. You will also need to enclose with your application your current US passport, and a signed statement. The statement must attest to the reasons you require a second passport, and to your understanding that lost or stolen passports must be expediently declared. The US Embassy in Germany provides this example statement for reference: https://de.usembassy.gov/wp-cont.... Strong applications are advised to also include a signed statement from your employer on company letterhead attesting to the same. If applying by mail, you must also include a check to cover the application fee.All that being said, I can find no evidence to support the claim that entrance stamps or visas from Pakistan, Bangladesh, or India would exclude you from entry to either of the other two, respectively.