This is a circuit topology I have used with success for a switched-gain amplifier with very well controlled bandwidth, using two conventional OPAMPs and an analogue multiplexer. It avoids some of the issues with the multiplexer, and even turns them to advantage. Note the component selection is arbitrary for illustration, you will need to choose appropriately.
U1A is wired as a non-inverting amplifier, U1B is inverting. The analogue multiplexer U2 and resistors R2-R10 act as a switched potentiometer. When input X7 is selected, the feedback resistance of the non-inverting stage is at the minimum value, while the input resistance of the inverting stage is at maximum: this gives minimum gain. As lower-numbered channels are selected, the gain of each stage is increased. By choosing suitable resistance values, you can get gains evenly spaced in dB.
Note that the gain is not affected by the multiplexer on resistance, which simply appears in series with U1A output resistance, so its effect is reduced by the negative feedback around the OPAMP. What may be less obvious is that the multiplexer capacitance (i.e. between Xn and GND) actually helps.
As the gain of each stage is increased, its bandwidth will be reduced because of the limited gain-bandwidth of the OPAMP. However, the parasitic capacitances, in conjunction with the gain-setting resistors, act as a cascade of RC low-pass filters. At minimum gain, all these filters appear in the input resistance to U2B, thus rolling off its gain at high frequency. At maximum gain, these same filters are removed from U1B's feedback network and instead act to reduce the feedback applied at high frequency around U1A. A judicious choice of resistor values can give a circuit bandwidth almost unaffected by the gain setting.
I found a gain range of around 30dB was practical with this circuit: you can cascade two to get your required range.
I suggest using the best OPAMP models you can get to simulate the blazes out of the design, tweaking resistor values as necessary to get the best results, then breadboard. For my application, I was working with a bandwidth of 2.5MHz, but I needed to control the phase response to within ±5˚ over the bandwidth. I found it necessary to add a few pF additional capacitance to ground from one of the taps - this didn't show up from the simulation results.
Oh, and watch the power rail decoupling. The PSRR of most OPAMPs is pretty dire at high frequencies, and feedback thorugh the supply rail can mess things up something rotten!