Yes — extension tubes and close-up filters can be used together, and combining them generally increases magnification by letting the lens focus closer. They affect the lens in different ways: extension tubes move the lens farther from the sensor, while close-up filters act like a magnifying glass on the front of the lens.

However, “better macro” does not always mean better image quality. Stacking them can make focusing distance very short, reduce light reaching the sensor, and make sharp focus harder to achieve. Image quality depends heavily on the quality of the close-up filter; cheap single-element filters often soften the image more than good achromatic close-up lenses.

For a budget setup, extension tubes are often a good starting point because they contain no glass, so they don’t directly reduce optical quality. Close-up filters are convenient and work especially well on longer lenses. You can combine both if needed, but expect more difficult handling and a shallower depth of field.