Bigamy is the act of marrying one person while being legally married to another. Polygamy is the practice or custom (often religious) of having more than one wife or husband at a time. Most states prohibit a party from having more than one marriage license at a time, and in most states bigamy is a crime.
In Texas, both bigamy and polygamy are prohibited by law. Bigamy is explicitly illegal under Texas Penal Code Section 25.01, which states that an individual commits an offense if they are legally married and they: (1) marry or purport to marry another person; or (2) live with a person other than their spouse in a state that recognizes that relationship as a marriage. Bigamy in Texas is typically considered a felony, and the severity of the charge can range from a third-degree felony to a first-degree felony depending on the circumstances, such as the age of the additional person one attempts to marry. Polygamy, which involves having more than one spouse simultaneously, is not legally recognized in Texas and is encompassed by the laws against bigamy. As such, any marriage license obtained while already married would be invalid, and attempting to obtain one could lead to criminal charges.