If the V_CE(sat) of a bias resistor built-in transistor (BRT) does not drop to the design target because of a heavy load, what can I do?

Figure 1 shows a simple BRT circuit. R_O is a pull-up resistor for the BRT, and Z_L is the load impedance. For the sake of simplicity, Z_L is considered an impedance (resistance) expressed as a real number.
In this case, while Q is on, the collector-emitter voltage must satisfy the low-level voltage requirement for the following circuit.

First, let’s consider a circuit without Z_L.
Without Z_L, the collector-emitter saturation voltage (V_CE(sat)) of the internal transistor (Q) is expressed as a function of the collector current (I_C):
    V_CE(sat) ≈ R_O * I_C

When Z_L is connected to the BRT, the combined impedance seen from the collector of the BRT is:
    Z = R_O // Z_L = R_O * Z_L / ( R_O + Z_L )　
The collector-emitter voltage (V_CE) due to this combined impedance is expressed as follows:
    V_CE = Z * I_C
V_CE must satisfy the low-level voltage requirement of the following circuit. Otherwise, it is necessary to increase the collector current by increasing the base current (I_b) of the internal transistor.
I_b can be increased in the following ways:
    1. Increase the input voltage (V_I).
    2. Replace the BRT with the one having a smaller R₁ value.
    3. Replace the BRT with the one having a larger R₂ value.