I am trying to filter a signal using a given FIR band stop filter. I have to implement a band pass filter. Assuming I want to get the signal between normalized cutoff frequencies [0.2,0.3] - can I use two band stop filters over the same signal - one for the range [0,0.2) and second for the range (0.3,1] ?
Yes, there's no reason why you couldn't do that. If you cascade two systems in series, the overall transfer function (and therefore frequency response) is the product of the two systems' individual responses. Therefore, you can apply the first filter to attenuate frequencies in the range $[0,0.2\pi]$, then the second will attenuate frequencies in the range $[0.3\pi, \pi]$. The result is that all frequencies except for those in the range $(0.2\pi, 0.3\pi)$ are attenuated, which looks a lot like a bandpass filter response.
Note: Don't take the choices of brackets/parentheses in the intervals above too seriously. Any realizable filter has a finite-width transition region, not instant transitions between passband and stopband.