R1 represents the signal source impedance, in this case 200 ohms. If R2 is 4 x 200 ohms = 800 ohms the conversion loss is the same as a single switch with signal integrating capacitor driven by a 25% duty cycle clock. If the clock's duty cycle is increased to 50% the circuit shows some conversion gain. One side of the switch is now effectively grounded (virtual gound of the opamp). The next thing would be to investigate increasing the source impedance that each switch sees.

Below is a two switch model with LT1115 op amps:

Below is a two switch model with LT1115 op amps: