First, what do you mean under the saturation of TEC ?

By the way, you can find usefull information about ionospheric responce to geomagnetic disturbances in many reviews or books, e.g. Mendillo (2006) Storms in the Ionosphere.. ; Kelley (2009) The Earth's Ionosphere.. ; Buonsanto (1999) Ionospheric Storms

The ionosphere is known to respond linearly during the ascending and descending phase of a solar cycle.Saturation as well as amplification of plasma density has also been observed around the peak. Since increased geomagnetic acivity affects the plasma and enhances or reduces the base level at that given time, increased geomagnetic activity ought to affect the plasma density even under the state of saturation or amplification.

The answer to this question can be illustrated using this simple physics illustration:

Since extra energy from the sun is release into the ionosphere during geomagnetic storm, this energy must be transformed into another forms of energy (law of conservation of energy) in the ionosphere which can cause ionospheric disturbance. Definite this might has an effect in the ionospheric parameters either in term of enhancement or depletion of the parameters with magnitude that is latitudinal dependent. I believe geomagnetic disturbance has nothing to do with saturation.

Ionosphere is a part of magnetosphere, so geomagnetic disturbances caused by compressed fast solar wind after solar flares has limited effect on polar ionosphere - magnetosphere system because of saturation of magnetospheric reaction for very big solar wind electric field and dynamic pressure during superstorms

Not only magnetosphere, but thermosphere and upper atmosphere should be included in this net. Recent studies show that forcing from below is very important for ionospheric dynamics during storms. Chemical composition changes, uplifting of thermosphere and etc.

Certainly, you are right, but question first of all is about saturation on effect of extramagnetospheric - solar wind - parameters, not intra. Last (intra ) also one should take into account, but initially - SW parameters and then -all you said

Saturation effect in ionospheric electron density is marked by ceasation in the ionization process due to photoionization or due to the electrodynamical process in the ionosphere. Geomagnetic disturbance is known to modify the drivers of ionospheric electron density. Hence, in theory, geomagnetic should influence saturation effect because saturation effect is a feature of the solar activity maxima and the frequency and intensity of geomagnetic disturbances could very significant on the saturation effect during this solar activity phase.

1) what do you call saturation?

2) Geomagnetic disturbances are the results of a) solar disturbances as CME, solar Flare, high speed solar Wind and also b) atmospheric disturbances.

For example a solar Flare produces a strong increase of ionization and ionospheric electric currents and as a consequence you can see the geomagnetic disturbance called a crochet.

Many geomagnetic disturbances depend of the ionospheric disturbances or magnetospheric disturbances