Offence under Section 494 (bigamy or second marriage) and Section 497 (adultery) may not be applicable in the facts stated by you. Moreover, the offence of rape may also not be attracted if the woman in live-in relationship has given her full consent with transparent knowledge of the fact of first marriage of the man (i.e., the man should not have concealed anything or misrepresented anything material).
However, living in a live-in relationship with another woman may perhaps amount to an offence under Section 498-A of IPC against the wife from the marriage of the man, since it may perhaps be considered as subjecting the wife to cruelty.
Further, if there is any wilful misrepresentation or concealment of a material fact to the woman in the live-in relationship, that may also amount to an appropriate offence depending upon the type and nature of the acts committed during such relationship and the false promises (for example, false promise of marriage), if any, given to such woman.
Other than these, there are ethical and moral issues.
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