@Stateless
@Remote(WhoAmI.class)
@RunAs("Admin")
@SecurityDomain("other")
public class Bean1 implements WhoAmI {

    @EJB(beanName = "Bean2")
    private WhoAmI singleton;

    public String getCallerPrincipal() {
        return singleton.getCallerPrincipal();
    }

}

@Singleton
@Remote(WhoAmI.class)
@SecurityDomain("other")
public class Bean2 implements WhoAmI {

    @EJB(beanName = "Bean3")
    private WhoAmI bean3;

    private String principal;

    @PostConstruct
    public void init() {
        principal = bean3.getCallerPrincipal();
    }

    public String getCallerPrincipal() {
        return principal;
    }

}

@Stateless
@Local(WhoAmI.class)
@RolesAllowed("Admin")
@SecurityDomain("other")
public class Bean3 implements WhoAmI {

    @Resource
    private SessionContext ctx;

    public String getCallerPrincipal() {
        return ctx.getCallerPrincipal().getName();
    }

}