Law 2.4.3
A side of the blade used for striking the ball shall be covered with either ordinary pimpled rubber, with pimples outwards having a total thickness including adhesive of not more than 2mm, or sandwich rubber, with pimples inwards or outwards, having a total thickness including adhesive of not more than 4mm.
ITTF Racket Coverings Technical Leaflet TF
A.Qualitative Criteria
1.3 Sponge
The use of sponge (i.e. cellular rubber) is governed by The Law 2.4.3.
Translucent red coverings may not be used over dark sponges or dark blades, and translucent black ones may not be used over light sponges or light blades.
1.4.3. Sandwich rubber
More than one layer of cellular rubber (sponge) is not permitted, even if the layers are of the same composition.
However, if the top sheet is translucent, then the layer underneath must be uniformly coloured; it is not permitted for a manufacturer's logo on the lower layer, or on the blade, to show through.
B. Quantitative Criteria
1. The racket covering
It should be noted in particular that:
Authorisation is given to the top sheet alone. Red and black top sheets with the same supplier and brand name must have the same geometry, properties, wording and numbering. The surface colours must be uniform. Such red and black top sheets do not require separate authorisation fees.
It is the player’s responsibility to limit the total thickness of his racket covering to no more than 4.0 mm, including top sheet, sponge and adhesive.
It is also his responsibility to ensure that a red top sheet does not become too dark when affixed to the sponge, or a black covering too light.
So as you can see, although the ITTF do not authorise sponges, there are still several limitations on the sponge you can use under your topsheet. You must make sure that the overall rubber does not exceed the thickness limitations, that red rubbers do not become too dark, that black rubbers do not become too light, and that the manufacturers logo on the sponge does not show through the topsheet.

