High pass and low pass filters are usually shelves, that is if you apply a low pass filter at a given frequency then you're losing frequencies about that cutoff frequency and can't get them back.
In order to get more than one limited range of frequencies, the most straightforward way is to use EQ.
One of the FMOD dsp types of DSP is FMOD_DSP_TYPE_PARAMEQ. For each frequency band you want to affect, create one FMOD_DSP_TYPE_PARAMEQ unit object and set the parameters appropriately. With EQ, you can't directly affect the range. Instead, you set a center frequency and the bandwidth or Q (more about EQ here: http://tweakheadz.com/EQ_and_the_Limits_of_Audio.html).
FMOD_DSP_TYPE_PARAMEQ
Enumeration
typedef enum { FMOD_DSP_PARAMEQ_CENTER,
FMOD_DSP_PARAMEQ_BANDWIDTH, FMOD_DSP_PARAMEQ_GAIN }
FMOD_DSP_PARAMEQ; Values
FMOD_DSP_PARAMEQ_CENTER Frequency center. 20.0 to 22000.0. Default =
8000.0.
FMOD_DSP_PARAMEQ_BANDWIDTH Octave range around the center frequency to
filter. 0.2 to 5.0. Default = 1.0.
FMOD_DSP_PARAMEQ_GAIN Frequency Gain. 0.05 to 3.0. Default = 1.0.
Remarks
Parametric EQ is a bandpass filter that attenuates or amplifies a
selected frequency and its neighbouring frequencies.
To create a multi-band EQ create multiple FMOD_DSP_TYPE_PARAMEQ units
and set each unit to different frequencies, for example 1000hz,
2000hz, 4000hz, 8000hz, 16000hz with a range of 1 octave each.
Here's a quick example (assuming you initialized FMOD and omitting error checking for brevity):
FMOD::DSP* dspObj;
systemPtr->createDSPByType(FMOD_DSPTYPE_PARAMEQ, &dspObj);
dspObj->setParameter(FMOD_DSP_PARAMEQ_CENTER, 500);
dspObj->setParameter(FMOD_DSP_PARAMEQ_BANDWIDTH, 0.2);
dspObj->setParameter(FMOD_DSP_PARAMEQ_GAIN, 3.0);
FMOD::DSPConnection* eq1Connection;
systemPtr->addDSP(dspObj, &eq1Connection);
systemPtr->createDSPByType(FMOD_DSPTYPE_PARAMEQ, &dspObj);
dspObj->setParameter(FMOD_DSP_PARAMEQ_CENTER, 1500);
dspObj->setParameter(FMOD_DSP_PARAMEQ_BANDWIDTH, 5.0);
dspObj->setParameter(FMOD_DSP_PARAMEQ_GAIN, 3.0);
FMOD::DSPConnection* eq2Connection;
systemPtr->addDSP(dspObj, &eq2Connection);
In DAW-land, you could route the audio from your source channel to two new aux channels and apply separate sets of high and low pass filters to achieve something sort of like this. However, I don't believe FMOD supports that kind of routing and it might raise performance concerns. Also, taking into account resonance the final mix using this approach could sound very strange.
Also, FMOD has the capacity to load some VSTs. If you're just exploring the API and not trying to implement FMOD for a full-on game, look at http://kvraudio.com and see if you can find some VSTs to do what you're trying to achieve.
I also don't know if it's possible to cut everything except for multiple frequency band sin FMOD. This is similar to the use case for a comb filter, but if you're doing this much synthesis you may be better off working on the sample level and implementing your own DSP effects by adding callbacks into a FMOD_DSP_DESCRIPTION structure.