In this paper, sequential and fixed sampling schemes are combined to estimate the parameters and quantiles of a two parameter binary response model. In the first stage of the proposed procedure, samples are sequentially observed to estimate two particular quantiles. Additional responses are then observed in the second stage at these two quantile estimates. Maximum likelihood estimators of the parameters and quantiles of the model are than produced using the combined samples from both stages. The asymptotic distributions of the estimators are derived. Asymptotic comparisons are made between the proposed procedure and a strictly sequential estimation procedure. A Monte-Carlo study is performed to assess the effectivness of the proposed procedure for finite samples. Recommendations are made concerning the number of observations to collect in each stage.