Absolutely! Needlepoint, like any art form, is adaptable and can be personalized to your own preferences - or can be made from materials in your own stash.
However, be aware that finished size and thread coverage on the canvas will change as well.
To find the finished size of a pattern, count the number of vertical and horizontal stitches. Divide these 2 numbers by the mesh count of the intended canvas to come up with the new size.
For example, a 100x100 stitch pattern on 10-count canvas will measure 10 inches square. The same pattern worked on 14-count wil measure just over 7 inches square.
While changes in canvas holes-per-inch versus finished size seems obvious, other changes may be unexpected.
Stitches can take on a different appearance based not just on the number of holes per inch, but also the thickness of thread used, and on the type of canvas used.
An example can be seen in this photo. The Woven Stitch on 14-count Mono Canvas covers the canvas well, while the same stitch on 14-count Penelope Canvas leaves gaps between the stitches.
When in doubt, work a small test swatch to see if the coverage is what you have in mind.