Selectively improve the frequency resolution of FFT (DFT)
You can compute any single FFT result bin using a complex Goertzel  algorithm or filter.

Realize however that if you want to compute a number of bins on the order of log N or greater (such as 10 extra bins with 10 Hz bandwidth and spacing), it may be faster to do the full longer FFT and throw away all the extra FFT result bins.

So just compute 2 FFTs of 2 different lengths and ignore all the unwanted results.