We consider a test which allows students to attempt a multiple-choice question multiple times (i.e., multiple attempts). The most extreme form of multiple attempts is the answer-until-correct (AUC) procedure. Previous research has demonstrated that multiple-attempt procedures such as AUC could potentially enhance learning and increase reliability. However, for multiple-choice items, guessing is still non-ignorable. Traditional models of sequential item response theory (SIRT) could model multiple-attempt procedures but fail to take guessing into account. The purpose of this study is to propose SIRT models for multiple-choice, multiple-attempt items (SIRT-MM). First, we defined a family of SIRT-MM models to account for the idiosyncrasies of items, answer options, and examinee behavior. We also explained how these models could improve person parameter estimates by taking into account partial (mis)information of examinees. Second, we conducted model comparisons between the SIRT-MM models, the graded response model, and the nominal response model. Third, we discussed how the item and person parameters can be estimated, and evaluated item and person parameter recovery of SIRT-MM models under different conditions through a simulation study. Finally, we applied the SIRT-MM models to a real dataset and demonstrated their utility through model selection, person parameter recovery, and information functions.