Designing a BJT transistor amplifier with a current gain greater than 1000?
As mentioned in the comments to your question, there are two simple beta-boosting configurations: Darlington and Sziklai. 

For both configurations the effective beta (current gain) is a multiplication of the betas of the two transistors. Below are the schematics for these two configurations.

pay attention that the resistor in both cases is not necessary but it helps to improve the slow response time of these configurations and prevents leakage current through Q1 from biasing Q2 into conduction. Also make sure to choose its value so as not to steal substantial base current from Q2. 







simulate this circuit &ndash; Schematic created using CircuitLab