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BNK Sharma, a well known scholar and author belonging to Dwaita school of Vedanta has written this in his book Advaita Siddhi vs Nyayamrita, an up to date appraisal.
Here's the excerpt
Is this true? Afaik Madhusudhana Saraswathi is one of the orthodox Advaiti, and other Advaitins would consider him as an authority. And his works are regarded as classics.
So did he depart and deviate from original opinion of Shankaracharya?
If so, on what did he differ?
Short answer:
The later advaitins had to answer the critics of the school. The main critic was against the concept of avidya and adhyasa. Madhusudhana Saravasti and others introduced new terms and provided much more details and interpretations. There was NO deviation from Shankara’s teaching but many points not explained in detail had to be explained. These have no implications on the final theory of ajata vada, where is no creation etc. and there is only Brahman. But as a philosophy and at a vyahavarika level, these had to be explained. This also has no effect on the sadhaka, who should not worry too much on the nature of the non-existent snake (whether it hooded, black, poisonous etc.) and who should try to get out of suffering of samsara. This Ignorance can only be destroyed by the attainment of the Knowledge of the Absolute, this destroys both Ignorance and its effects -- Adhyasa and the world and Samsara. But then why did avidya and adhyasa arise in the first place?
Detailed answer on the avidya and adhyasa. Objections and rejoinders.
All schools of Vedanta agree that there is One Supreme Reality. Universal experience testifies to the existence of a world. The question then arises, how did this world come about?
The difficulty the Advaitin has is that he holds the Absolute Reality to be ever free from all qualities (Nirguna) and Non Dual. How could the world arise from such an entity? The answer is avidya.
Mayeda in his introduction to his book , 'A Thousand Teachings by Shankara".
3A; A Theoretical defect in Avidya (Adhyasa) Certainly the most crucial problem which Shankara left for his followers is that of Avidya. If the concept of Avidya is logically analyzed, it would lead the Vedanta philosophy toward dualism. As we have seen Avidya is the mutual superimposition of the Atman and non-Atman. If so, Avidya would come to be logically untenable. Shankara himself is aware of this fact and points it out in the pupil's question to his teacher: 'Is it not experienced that the thing which is superimposed upon something else, through Avidya does not exist in the later-for example, silver does not exist in the mother-of-pearl nor a snake in a rope, Likewise if the body and Atman are always mutually superimposed.. then they cannot exist in each other at any time….this being the case it would follow as a result that neither the body nor Atman exist. And this is not acceptable as this is the theory of the nihilists. For this reason the body and Atman are not mutually superimposed. (Upadeshasahasri 2-2-555).
That's why when the student asks:
Your Holiness, is the mutual superimposition of the body and Atman made by the composite of the body and so on or by Atman? (Upadeshasahasri II,2,62) I am merely the composite of the body and so on, then I am non-conscious, so I exist for another's sake; consequently, the mutual superimposition of body and Atman is not effected by me. If I am the highest Atman different from the composite [of the body and so on], then I am conscious, so I exist for my own sake; consequently, the superimposition of body which is the seed of every calamity is effected upon Atman by me who am conscious. (Upadeshasahasri II,2,84)
The teacher concludes:
You are right. [You] have no fault. The fault is only avidya as I have said before. (Upadeshasahasri II,2,85)
It is not possible for us to judge whether Sankara affirms or rejects the pupil's statement quoted above that avidya cannot have one's own Atman as its object. As in the case of the locus of avidya, Sankara refrains from giving a clear-cut reply to the problem of the object of avidya.
Suresvara stresses the locus and the object of avidya and concludes that Atman is both the locus and the object of avidya. His view is accepted by Sarvajnatman, and further by Prakasatman of the Vivarana school of the Advaita Vedanta. However, Madanamisra assertes that the locus of avidya is jiva, the individual atman, and that the object of avidya is Brahman, which is concealed by it. His view is accepted by Vacaspati misra, the author of the Bhamati, and forms the fundamental standpoint of the Bhamati school of the Advaita Vedanta. This is one of the basic differences between the two schools.
Later Advaitins raised avidya to the status of a metaphysical and eternal substance or a cosmic power (Sakti). They characterized avidya as indefinable as real or unreal (sad-asad-bhyam-anirvacaniya) belonging neither to the category of being nor non-being.
Avidya has two powers: avarana shakti (the power to completely cover the absolute reality) and vikshepa shakti (the power to project the unreal world). It is this Ignorance that is said to be the cause of the dualistic world as well as transmigratory existence (Samsara) as well as Adhyasa-the misconceptiontion of superimposing the Self and the Non-Self. This Ignorance is neither describable as existent nor as non-existent (sat-asat anirvachiniya) nor can it said to be either the same as the Absolute nor different from the Absolute. This is explained in great detail by Madhusudhana Sarasvati.
Avidya works on its object, i.e., Atman, and projects it in various forms illusorily. It is adhisthana that is Brahman-Atman and is the object of avidya. On the other hand, aadhara is the locus of superimposition. In the case of the false knowledge of a piece of mother-of-pearl ("This is silver"), the mother-of-pearl is adhisthana and the adhara is the referent of the term "this" which is the locus of superimposition. Adhisthana and adhara are essential both different. Now, are both of them unreal, or only one of them unreal? If both are unreal, then the world is completely an illusion, then it is nihilism or some school of Buddhism. Sarvajnatman, the disciple of Surveshvara Acharya, introduced these terms and argues only one of them is real and trying to solve the problem of mutual superimposition.
Thus the adhyasa conundrum raises the following questions.
a) Brahman does the superimposing. [This is a problem because then Brahman is changing and cannot be sat].
b) adhyasa is an 'independent' process outside of Brahman. [This is a problem because then Brahman is no longer One without a second]
c) we ourselves do it. [If 'we' are ourselves a superimposition, it would be a superimposition superimposing and then who would produce the first superimposition]
Which of the above options are correct? Why?
Thus, in order to address these questions and other details on avidya etc., many concepts had to be discussed in detail. Starting from Sarvajnatman, Sri Harsha, Madhusudhana Sarasvati, Appayya dikshitar etc. This is especially required for polemical debates to establish the epistemological and ontological applicability of advaita. However, there is no fundamental deviation from the philosophy developed by Adi Shankara that Ignorance can only be destroyed by the attainment of the Knowledge of the Absolute which destroys both Ignorance and its effects -- Adhyasa and the world: thus Samsara.
