Simultaneous sampling or doubled output rate with two LTC2400s
1) These 24-bit ADCs are vulnerable to trash from VDD, as are the VREF sources; for quietest performance, insert 1 ohm or 3.3 ohm resistors, in series, in the VDD PCB traces to both the ADC and your VREF. Why? at high frequencies, the opamps inside the ADC have no ability to reject power supply rash; its your job to insert R+C low_pass_filters into the VDD paths. For ADC and for VREF.

2) Consider that VREF signal ----it is a precious signal, right. So consider how to keep it away from trash, from Efields, from Hfields. SwitchRegs fields are not affected by standard thickness PCB foil; you may need to surround your 24-bit system by some steel, for cleanest results.

3) These 24-bit ADCs are vulnerable to noise-floor degradation by trash injected on the digital interface pins.

To learn more, consider the LTC2410, which has 7 SEVEN Ground pins, versus the LTC2400 with ONE Ground pin. Those additional 6 pins are used for substrate shields, that collect trash and separate the analog regions from the digital regions.

Also  the LTC2410 has a digital-trash-quelling circuit ON THE PCB. 
Read the LTC2410 datasheet and examine that circuit. You will note the interface buffer
has PRIVATE POWER, not to be shared with the ADC or the MCU.

Summary ---- do not directly wire the 24-bit ADC digital pins to a MCU.

Even if you put those MCU pins into TriState, the output capacitance of the MCU Drivers is injecting trash into the ADC, and the primary exit path will be the GND pin.

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Look at Figure 57 (5-7) near end of datasheet.

Discussing digital noise injected from MCU (the usual +- 0.5 volt trash visible on both Logic_0 levels and Logic_1 levels, because even when output pin of MCU is constant, the MCU is internally clocking as executes the program), how much can MCU internal activity upset the LTC2410?

Math --- assume +-0.5 volt ground bounce and VDD bounce inside the MCU, with 1 nanosecond rise and fall times; this is about 200 MHz Ringing. Assume output capacitance of the MCU pin driver is 10pF. (We'll assume all the charge thru that 10pF makes its way into the substrate of the 24-bit ADC.)

Assume the Inductance of the LTC2410 Ground path is 5 nanoHenry.

We will compute the current coming from the MCU, and then have that current pass thru the Ground inductance of the 24-bit ADC.

Current =  * dV/dT = 10pF * 0.5v/1nS = 10 * 0.5 * pico/nano = 5 milliamp

(had been in error, initially computed 0.5mA)

Now for the Ground upset, inside the LTC_2410:

V = L * dT/dT = 5nH * (5mA /1nanoSecond) = 25 milliVolts

The Ground Upset is 25 millivolts yet you expect 1 microvolt performance.(had previously been 2.5 milliVolts)

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Note the LTC2410 datasheet Figure 57 has a HEX INVERTER and a bipolar transistor and some resistors, and PRIVATE VDD for the HEX INVERTER.

Thus LTC does not want their Evaluation PCB performance to be upset by whatever off-PCB MCU is connected.

The math I showed you, predicting 25,00 microVolts of Ground trash induced into the LCT2410, has a purpose. We can predict how to solve this problem, because we have the math.

Notice the computation uses dV/dt and then dI/dT. This double derivative is crucial ---- if we slow down the ringing by 2X, we'll get a 4X reduction in the ringing amplitude. However we cannot affect the ringing frequency because the MCU does that without caring about external components.

Our only solution is to install low-pass-filters in the incoming and outgoing digital-interface pins. This might include Fin, if you use that.

I would use "T" filters in each of the 3 data-movement lines: use 2 of 1,000 ohms in series, and a 1,000pF cap to ground at the midpoint of the 2 resistors.

Thus you need 6 resistors, and 3 capacitors.

Notice the SLOW time constant ---- 1,000 nanoseconds. This guarantees a 60dB attenuation of the MCU trash. Your highest datarate may be only 500,000 bits per second.

Your question about Vin- connection? You could ground that, but to what "ground"? If you want best performance, given you have offered no information on your sensors, why not extend both Vin+ and Vin- out to your sensor? Notice the LTC datasheet has several pages on differential inputs.

Read and understand the datasheet. Don't be shy about calling/emailing ADI for advice.