Shown below are examples of circuits that illustrate how to widen the hysteresis range in an application that uses a detection voltage alteration circuit.

Figure 1: Nch Open Drain Output
Output is pulled up to VDD2

Figure 2: Nch Open Drain Output
Output is pulled up to VDD2 where DD2 > VDD1
Looking at Figure 1, Diode D1 will be needed to prevent a reverse current from RUP to R2 and to R3. Let us assume that the detection voltage in IC setting to be -Vdet, hysteresis in IC setting, VHYS, and forward voltage of D1, Vf. When detection is made, the voltage obtained by dividing VDD by R1 and R3 is compared with the detection voltage in IC setting,
When VDD lowers below the operational detection voltage and the level of the output becomes low, the circuit illustrated in Fig. 1 will become equivalent to the circuit shown in Fig. 3.

Figure 3: Equivalent circuit when VDD is below operational detection voltage
In a detection state, R2 and Vf are input to R3 in parallel and the operational release voltage and operational hysteresis range will become as follows

The same values can be used with the circuit illustrated in Fig. 2 also.
As a precaution for R1 and R2 setting values, R1 < 75kΩ should be set as a countermeasure for oscillation. Detection voltage will deviate by current consumption x R1 voltage the larger R1 is, to deteriorate the detection accuracy. Therefore, set values for R1 and R2 are recommended to be as small as possible (about several kΩ).