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Covariate-adjusted randomization (CAR) can reduce the risk of covariate imbalance and, when accounted for in analysis, increase the power of a trial. Despite CAR advances, stratified randomization remains the most common CAR method. Matched Randomization (MR) randomizes treatment assignment within optimally identified matched pairs based on covariates and a distance matrix. When participants enroll sequentially, Sequentially Matched Randomization (SMR) randomizes within matches found "on-the-fly" to meet a pre-specified matching threshold. However, pre-specifying the ideal threshold can be challenging and SMR yields less-optimal matches than MR. We extend SMR to allow multiple participants to be randomized simultaneously, to use a dynamic threshold, and to allow matches to break and rematch if a better match later enrolls (Sequential Rematched Randomization; SRR). In simplified settings and a real-world application, we assess whether these extensions improve covariate balance, estimator/study efficiency, and optimality of matches. We investigate whether adjusting for more covariates can be detrimental upon covariate balance and efficiency as is the case of traditional stratified randomization. As secondary objectives, we use the case study to assess how SMR schemes compare side-by-side with common and related CAR schemes and whether adjusting for covariates in the design can be as powerful as adjusting for covariates in a parametric model. We find each SMR extension, individually and collectively, to improve covariate balance, estimator efficiency, study power, and quality of matches. We provide a case-study where CAR schemes with randomization-based inference can be as and more powerful than Non-CAR schemes with parametric adjustment for covariates.