Types of Woman Not to Marry in Islam
Question

Are there any instances in Islam where it is permissible to marry a woman in some cases and it is not permissible to marry the same woman in other cases?
Praise be to Allah.
It is prohibited to marry a woman who is in `Iddah following the end of a marriage by divorce or death to another man, because Allah says (interpretation of the meaning):

“And do not consummate the marriage until the term prescribed is fulfilled.” [Al-Baqarah 2:235]
The wisdom behind that is that there is the possibility that she might be pregnant [from the first husband], and it would result in the sperm being mixed and the lineage being confused (i.e., if he were to marry her before the ‘Iddah was over).

It is prohibited to marry a woman who has committed fornication or adultery if she is known to have  done that, until she repents and completes her `Iddah, because Allah says (interpretation of the meaning):

“and the adulteress –fornicatress, none marries her except an adulterer — fornicator or a Mushrik]. Such a thing is prohibited to the believers (of Islamic Monotheism).” [Al-Nisa’ 24:3]

It is prohibited for a man to marry a woman whom he has divorced three times until she has been married to another man in a valid marriage which has been consummated, because Allah says (interpretation of the meaning):

“The divorce is twice … And if he has divorced her (the third time), then she is not lawful unto him thereafter until she has married another husband…” [Al-Baqarah 2:229-230]

It is prohibited to marry a woman who is in the state of Ihram for Hajj or `Umrah until she has exited the state of Ihram.
It is prohibited to marry to two sisters at the same time, because Allah says (interpretation of the meaning):

“Forbidden to you (for marriage) are: … and to combine two sisters (in marriage, simultaneously).” [Al-Nisa’ 4:23]

It is also prohibited to marry a woman and her paternal or maternal aunt at the same time, because the Prophet (peace and blessings of Allah be upon him) said: “Do not be married to a woman and her paternal aunt or a woman and her maternal aunt at the same time.” (Al-Bukhari and Muslim)

The Prophet (peace and blessings of Allah be upon him) explained the reason behind that when he said, “If you do that, then you have broken the ties of kinship.” That is because of the jealousy that exists between co-wives, and if one of them is related to the other, the ties of kinship between them will be cut. But if a woman is divorced and her `Iddah is over, then her sister, paternal aunt and maternal aunt become permissible for marriage (to that man), because the reason for the prohibition has ceased to exist.

It is prohibited to marry more than four women at one time, because Allah says (interpretation of the meaning):

“then marry (other) women of your choice, two or three, or four.” [Al-Nisa’ 4:3]
The Prophet (peace and blessings of Allah be upon him) commanded those who were married to more than four women to divorce some of them when they entered Islam.
And Allah knows best.