Is this a photo you're importing? It sounds like you're resizing up to
do an overpaint. Is this correct? If so, why does the pixelation matter? If you're overpainting then a bit of pixelation won't make a difference (not that I've ever used that function so I stand to be corrected).
Regarding the resolution of 240 - you mean DPI, right? DPI makes no difference at all to the digital image. It doesn't matter whether you work at 5dpi or 5000dpi. DPI only applies to printing and refers to the number of pixels that will span an inch of printed image.
One reason people get confused about DPI (and 99% of people are) is because when you change DPI the s/w package often assumes you want to keep the print size the same, and therefore changes the pixel resolution for you. In most pacakges you can turn this off via a checkbox (normally something like "Preserve Image Size") which stops the s/w "helping you out" by resizing your image when you change the DPI (and vice-versa).
At a guess (as I'm not sure what you're doing) I'd say you need to
a) Decide what DPI you want to print at. Let's say 240 (as your original image is already 240)
b) Import your image. Resize it from 2760x3720px (which, if it's 11.5x15.5 inches @ 240DPI, it is now) to 5760*7200px (which is 24x30" @ 240DPI). Make sure you have modified the checkbox so DPI doesn't change when you resize.
c) Your image will now be resized and slightly pixelated from the upsizing. Use this in whatever way you need and print it out.