Overlay

is the most popular option amongst all fabric repairs as it is the lowest risk. But it carries the following considerations

1. Overlay is done typically using brand new minky or cotton, as a hand-sewn wrap over the original. Note that it is impossible to color match exactly. Hence please decide on the right color for you. 
2. Minky is semi-directional. Cotton may be directional. The doctor will decide on the best direction to use based on the shape of your plush. You will not be receiving any information on the direction of choice, nor be able to make a decision on the direction. If it looks strange to you, you are to raise it up to the doctor at the earliest notice once spotted. 
3. Overlay adds new fabric onto your plush and adds to the weight and size. 
4. Overlay hides the original fabric underneath. You will no longer see the state of the original fabric. It may continue to further degrade underneath as part of its age. Opt for a single-sided overlay if you do not want a complete wrap. 
5. Partial overlay may make parts of your plush higher than others due to the thicker layer. 
6. Overlay will also make the skin feel thicker (double layer)

Note that this double layer also makes it harder to dry when washed.

Variations

Applique Overlay (Eyes)

Commonly used to overlay across felt eyes that have degraded over time

1) The new pair of eyes will be the thickness of the original (as a thick felt has much higher durability), and thus, when sewn on top of an existing pair of eyes, the eyes will be double the thickness, and when viewed from the side, they will be higher

2) We cannot safely remove the old pair of embroidered eyes, which we will hide below the new embroidered set

3) We manually cut out the embroidered new pair of eyes from the felt base. Hence, there will be a small felt border around the embroidered section that is left over. This border is to prevent the embroidery from fading

4) The new pair of eyes will be larger than the original pair by about 10 to 20% to cover the existing pair smoothly

5) As this new pair will be hand-sewn above the existing set of eyes; these stitches from the hand-sewing may be visible

6) These new pair of eyes will continue to fade and be damaged with time, as this is a characteristic of felt as a fibre fabric. The only solution is a full embroidered eye, which will look very different from the original.

7) The fix may not be as perfect for more complex overlays where the shape of the applique has pointed edges and if there is detailing (like eyebrows, eyelashes,  eyeshadow).

8) All hand sewing risks apply as this method uses hand sewing.