Nothing obliges you to follow a numbered canvas exactly, and plenty of people want to make one their own. The trick is knowing which changes a design can absorb and which ones quietly destroy it, because they are not obvious and the difference is not a matter of taste.
The one rule worth knowing

A painting is held together by value, meaning how light or dark each area is, far more than by hue, meaning which color it is.
Depth, form and the sense of light all come from the pattern of lights and darks. Hue sits on top of that and can be moved around a great deal without anything falling over.
So the rule is: change the hue freely, change the value carefully or not at all. Repaint a red barn blue and the picture still works, as long as the blue is the same lightness as the red was. Repaint that same barn pale cream and the whole composition collapses, because the thing that anchored the picture has stopped being the darkest object in it.
Squint at the design image before you change anything. Squinting removes hue and shows you the value structure, which is exactly what you must not disturb. The color wheel covers the relationship in more detail.
Changes that work
Swap a color at the same value
The safest and most effective change. Mix your replacement, put a stroke of it on paper next to a stroke of the original, let both dry, and squint. If they read as the same lightness, you can substitute it anywhere that number appears.
The important part is being consistent. If a color appears in eleven regions, change all eleven or none.
Shift the whole palette's temperature
Warming or cooling every color slightly, by adding a touch of the same warm or cool to each, changes the mood of an entire painting without touching the structure. A late-afternoon version of a midday scene is a genuine transformation and it is entirely safe.
Add a light source
Lit windows in a cabin, a lamp on a porch, a brighter moon. Small warm marks in a cool scene are always convincing because that is how real light behaves, and because they are small they cannot disturb much.
Vary the paint thickness
Underrated and free. Lay the paint a little more thickly in the foreground and thinly in the distance. Real distance flattens texture as well as color, so this reinforces depth rather than fighting it, and it makes a numbered canvas look markedly less flat.
There is more on this in our guide to adding texture and depth, which covers the other ways to break up a flat section without repainting it.
Metallics, but only in the smallest places
A touch of gold or copper on a lit window, a moon path or a brass detail can be lovely. Used across a broad area it goes wrong quickly, because a metallic changes value depending on the angle you view it from, which is precisely the property you did not want to introduce. Keep it to the smallest and brightest elements only.
Paint the edges of the canvas
On a framed canvas the side faces are usually bare white primer, and they are visible from every angle except straight on. Continue the picture around them, or paint all four a single quiet color drawn from the painting. It takes ten minutes and it is the change people notice most.
Add one small element of your own
A bird in the sky, a boat on the water, the silhouette of a dog on the shore. Practice it on paper first, keep it small, keep it in silhouette, and put it somewhere with a plain background behind it. One well-placed addition looks intentional. Three look like graffiti.
Sign it
Small, lower right, in a color already present in the painting rather than in black, and before varnishing. Put the date and the design name on the back in pencil while you still remember them.
Where personalizing goes wrong
Changing values. Covered above, and it is the one that matters. Lightening something dark or darkening something light flattens the picture and there is no getting it back.
Glitter over large areas. It scatters light unevenly, it changes the apparent value of everything it covers, and it cannot be removed. If you want sparkle, use it the way you would use a metallic: on the smallest bright things only.
Collaging photographs onto the canvas. It seems like the obvious way to make a painting personal and it rarely survives contact with reality. Photo paper yellows, the edges lift, varnish will not sit evenly over two different surfaces, and the join always shows. If you want a photograph in a painting, the answer is to have the photograph become the painting rather than be stuck to one. The smaller ways to personalize a canvas — edges, signature, framing — are worth doing either way.
Blending hard across every border. Some softening at the edges of clouds and water genuinely helps. Doing it everywhere dissolves the drawing that was holding the picture together, and a numbered canvas has no other drawing underneath to fall back on.
Running out. Mixing your own colors means using the kit paints faster, and mixing a matching batch a second time is very hard. There is a matched extra paint set for every design if you need more of the originals.
Test before you commit
Anything you are unsure about can be tried on paper, or on the back edge of the canvas, or on the wrapped side of a framed canvas where nobody will look. Let it dry fully before judging, because acrylic darkens slightly as it dries and a color that looked right wet often does not.
And if a change turns out badly, it is recoverable. Let it dry completely, then paint the original color back over it in two thin coats. Acrylic is opaque and forgiving. Do not attempt to remove anything with solvent.
The most personal version
All of the above is decorating somebody else's design. If what you actually want is a canvas of your own subject, Custom Paint by Numbers builds one from a photograph you send: your house, your dog, the view from somewhere that matters. The design, the divisions and the paints are all made for that image, which is a different and better thing than adapting a stock one.
When the painting is done, our guide to framing it well covers the finishing, and the full range of designs is here.