When using JUnit’s @Parameterized, can I have some tests still run only once [duplicate]

You could structure your test with the Enclosed runner.

@RunWith(Enclosed.class)
public class TestClass {

    @RunWith(Parameterized.class)
    public static class TheParameterizedPart {

        @Parameters
        public static Object[][] data() {
            ...
        }

        @Test
        public void someTest() {
            ...
        }

        @Test
        public void anotherTest() {
            ...
        }
    }

    public static class NotParameterizedPart {
        @Test
        public void someTest() {
            ...
        }
    }
}