Have done both series and parallel.
In parallel used separate TXV (cheap on ebay or surplus), totally different evaporators, one conventional air, the other water tube in tube. If cold enough to freeze up the air coil, the water coil handled the entire load (air txv basically shuts off). Like others have said, you do need to use 2 TXV with sense bulb a foot or more ahead of the junction on the suction line.
Have also put a 4T air evap on a 2T compressor, which is basically what you are doing in adding a series evap. TXV is so much more efficient than cap tube that you should use TXV for series connected evaps also, but only one evap needed.
Another advantage of the series connection is that the coil will not freeze up until air temp is about 35F if evap overall large enough..
Other part is to oversize the condenser, that way part of the condenser works as a supercooler. Only disadvantage there is that output air (or water) temp is lower; but the lower temp means higher efficiendy.
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