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It would probably help if you defined your terms

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The "box" ISO rating for a film indicates how sensitive to light it is. If you set that speed on your meter, use the meter in a standard way, don't have a filter on the camera, set your camera and expose the film at the settings recommended by the meter, you should end up with a normally exposed film.
Then if you develop the film according to the manufacturer's recommendations, you should end up with normal negatives.
You are asking here about changes to "normal".
First, adding a filter with a filter factor of 3 will result in an under-exposed negative, unless you adjust the settings on the camera. The best way to prevent that under-exposure is to increase the exposure settings by the appropriate amount - 3x the exposure time being the most accurate.
If that change in exposure isn't possible, you can partially compensate for the under-exposure by adjusting the development. A so called "push" development doesn't really help much with the under-exposure itself. Instead, it increases the contrast. That means that although you will still lose detail in the shadows and lower, lower mid-tones (the result of under-exposure), the increase in contrast will make lower mid-tones and mid-tones look better in the results. Unfortunately, the push will often also make the highlights look worse as well, but that is part of the trade off.
Note that the under-exposure of the film is not a "push". Increasing the development and therefore the contrast is a push.
So if your goal is to make up as much as you can from the losses due to under-exposure, a "push" development corresponding with 1.5 stops will help some. I'll let those who use a lot of HP5+ pass on their advice with respect to how much extra development works best. I expect that they would like to know what type of developer is being used and, most importantly, what the subjects are and the lighting is like where you intend to photograph. Under-exposure and a push development works much, much better with even lighting and moderate contrast.