@Mizike It IS possible, but terribly uncommon and expensive. IT also doesn't give you the full benefits of getting more dynamic range from the amp you are using. Also, since this would be a high-pass filter, you would be adding some rather high capacitance values in series with the entire speaker. Expensive to do with good quality parts.
What you really want is a line-level crossover. This is easy to do with a preamp amp combo, or with any integrated that has a pre-out and in.
Not all integrated units do this.
Among the best and least expensive solutions are the miniDSP units. They include crossover and EQ all in one.
Your best solution right now may be to run the main speakers "full range" and then add a miniDSP to the sub. This gives you the full quality of sound that your gear has, plus EQ and filtering to the sub.
One more tip. If your main speakers are ported, plug them before integrating with a sub. This will slightly raise the -3dB point, but more importantly, reduce cone excursion, which will give you overall much better dynamic range with lower distortion.