Please clarify in detail with reference to the Qur'an & Hadith, if it is allowed to marry wife's own sister keeping the wife in marriage as it is? Please also explain the rationale & logic of the instruction associated.
The Holy Qur'an has explicitly prohibited marrying two sisters at a time. The Almighty says:
You are prohibited to marry your mothers, daughters, sisters, paternal aunts, maternal aunts, daughters of your brothers and sisters, your forester mothers and sisters, mothers of your wives, your step daughters raised under you born of your wives with you have lain- if you have not lain with their mothers then marrying them incurs no sin - wives of your sons, and two sisters at the same time except for what has been done in the past. (4:23
The Holy Qur'an has not explained the reason of this prohibition just as it does not mention the reason of prohibition of marrying one's daughter or mother. I think we may not seek logic behind everything mentioned explicitly in the Qur'an after we have acknowledged the Almighty as our Law Giver and affirmed that He is the author of the Qur'an.
Scholars have however held that since envy and competition have always existed between two women under one person there is a great chance that the two sisters married to one person tread the same path and disregard the sacred relationship of sisterhood between them. It is only to maintain the sanctity of the original relation between them that they are not allowed to be married at the same time.
This is however is the view of the scholars . God knows best.