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One op amp will have to be dedicated to setting the gain, one for the lowpass stage and one for the highpass stage. You are right, three will be needed.
Start by deciding what order (determines the roll off past cutoff) and what passband response you want. Chebyshev would be a good choice for your situation since it gives a pretty high roll off. Butterworth is more common and it might be easier to find the gain tables for this. Then select the gain for each stage from a reference table which you will find in most texts on the subject.
Generally, active filter gain is what is known as “realizable to a constant”. This means that once the order and response (Butterworth, etc.) are set, the gain is fixed to a particular value and cannot be changed because it is the only gain which will give the desired response. The designer has to accept this. The common solution is to follow the filter with a buffer amplifier and use that to set the gain.
For example, a filter may give a gain of 1.7 and you want to adjust this to a gain of 4. The buffer gain would be 4/1.7 = 2.35 and the overall gain is now 1.7×2.35 = 4 in the passband. You could use a buffer amplifier with variable gain to set the overall gain to whatever you want.
This sounds complicated because it is. That’s why people spend a long time learning how to design filters. I regret that I cannot just point you to a circuit that will work for you, but if this is a class assignment it was designed to provide a learning experience and you will need to study the topic. I taught this subject and it required 20 hours of lecture and lab time for my students to understand the topic so they could do what you want to do. Don’t give up on this, just be willing to spend some time on it.
I hope my suggestons are helpful.