Tex. R. Civ. P. 233
Except as provided below, each party to a civil action is entitled to six peremptory challenges in a case tried in the district court, and to three in the county court.
Alignment of the Parties. In multiple party cases, it shall be the duty of the trial judge to decide whether any of the litigants aligned on the same side of the docket are antagonistic with respect to any issue to be submitted to the jury, before the exercise of peremptory challenges.
Definition of Side. The term "side" as used in this rule is not synonymous with "party," "litigant," or "person." Rather, "side" means one or more litigants who have common interests on the matters with which the jury is concerned.
Motion to Equalize. In multiple party cases, upon motion of any litigant made prior to the exercise of peremptory challenges, it shall be the duty of the trial judge to equalize the number of peremptory challenges so that no litigant or side is given unfair advantage as a result of the alignment of the litigants and the award of peremptory challenges to each litigant or side. In determining how the challenges should be allocated the court shall consider any matter brought to the attention of the trial judge concerning the ends of justice and the elimination of an unfair advantage.
Tex. R. Civ. P. 233