The answer in Texas is "yes" in state court but "no" in federal court.
Comment 11 to Texas Disciplinary Rule 1.06 states: "Ordinarily, it is not advisable for a lawyer to act as advocate against a client the lawyer represents in some other matter, even if the matter is wholly unrelated....However, there are circumstances in which a lawyer may act as an advocate against a client, for a lawyer is free to do so unless this Rule or another [disciplinary] rule is violated. For example, a lawyer representing an enterprise with diverse operations may accept employment as an advocate against the enterprise in a matter unrelated to any matter being handled for the enterprise if the representation of one client is not directly adverse to the representation of the other client."
Under this rule, for example, a lawyer practicing in a large multi-office firm likely would not be prohibited from being adverse to a client for whom his firm was doing completely unrelated work in an office of the firm on the other side of the world.
Federal courts sitting in Texas, though, follow the Fifth Circuit, which itself follows the law under the ABA Model Rules of Professional Conduct. Those rules, as interpreted by the ABA committee which issues formal ethical opinions for the ABA has a "per se" rule that prohibits being adverse to a current client under any circumstances. In an opinion of that committee in 1995, for instance, it stated: "All members of this committee agree that a lawyer may never take a position directly adverse to a client...no matter how minor the matter and no matter how distant geographically, by industry or personnel, the new proposed representation is from the original one the lawyer is handling. Not only is that the rule, but that is what the rule should be." (Formal Opinion 95-390, 1995)