I have some high-quality RAW files.

This is important. Let us move on.

I need to have them printable at about twice the size I get with the ppi set to 240.

I guess the 240 ppi is a preset of the camera... Well, you can modify that value to whatever value you need.

Normal people, won't see a difference on a 100ppi photo and a 200ppi at 30cm except in some real little-micro-tiny details or at really close range (less than a feet).

The question is how far normal viewers will be? If you double the distance you can cut in half the resolution.

(This images have an error, it says dpi instead of ppi)

Now. If we start with a 300ppi file viewed at 30 cm we can start making some numbers.

In my experience, the expected viewing distance is somehow equal to the largest size of your photo.

But let us assume that you really need to resample an image. That is a matter of taste.

This test has some time but you can compare different software. The first image is a resize without any resampling. The second one with a Lanczos algorithm, which is similar to the bicubic one. And the other two are from popular resamping software. Benvista and Reshade.

In my opinion, a simple "bicubic sharpen" on Photoshop is good enough. You can use an additional sharpening if you need.

My recommendation is that you just should use round numbers. Resample at 200%, not at 187% for example.

I would never resample anything more than 200%. For a blurred background I could go for 300%.