The primary purpose of a dose-finding trial for novel anticancer agents is to identify an optimal dose (OD), defined as the tolerable dose that has adequate efficacy in unpredictable dose-toxicity and dose-efficacy relationships. The FDA project Optimus reforms the paradigm of dose optimization and recommends that dose-finding trials compare multiple doses to generate these additional data at promising dose levels. The backfill is helpful in settings where the efficacy of a drug does not always increase with the dose level. More information is available at these doses by backfilling patients at lower doses while the trial continues to explore higher doses. This paper proposes a Bayesian optimal interval design using efficacy and toxicity outcomes that allows patients to be backfilled at lower doses during a dose-finding trial while prioritizing the dose-escalation cohort to explore a higher dose. A simulation study shows that the proposed design, the BF-BOIN-ET design, has advantages compared to the other designs in terms of the percentage of correct OD selection, reducing the sample size, and shortening the duration of the trial in various realistic settings.