Question about the 3-transistor current mirror
I'll draw up the schematic you are talking about:







simulate this circuit &ndash; Schematic created using CircuitLab

Rather than just tell you the answer (I will, but allow me a moment), let's start by just laying out the nodal equation for \$V_x\$ shown in the schematic:

$$\frac{V_x}{R_2}+I_{B_1}+I_{B_2}=I_{E_3}$$

Adding \$R_2\$ makes only one difference here. There are two directions to head, in considering "why" it's added.

One direction is to focus on the impact on \$Q_3\$: (1) Increased emitter current; and, (2) reduced \$r_e=\tfrac{k T}{q I_C}\$; and, (3) The ability to set \$Q_3\$'s emitter current so that it is relatively independent of the base currents for \$Q_1\$ and \$Q_2\$.

The other direction is to focus on the impact of "current in" and "current out" of the node. I think it is this latter option that matters more here.

Imagine that there is some unmanaged capacitance sitting at \$V_x\$ (to \$V_-\$.) \$Q_3\$'s emitter can charge up this capacitance up quite actively, having access to the current through \$R_1\$ multiplied by its \$\beta_{Q3}\$. But it can only be discharged through the relatively much smaller base currents (the same current through \$R_1\$ but this time divided by \$\beta_{Q_1}\$ and \$\beta_{Q_2}\$.) This asymmetry leads to an undesirable response to higher frequency changes.

Adding \$R_2\$ provides a separate way to sink current out of the node and to help balance the ability to sink and source current at \$V_x\$.



This is also achieved another way that you may also encounter:







simulate this circuit



None of these are high precision circuits for discrete designs. They lack careful consideration of operating temperature differences, beta mismatch, and \$V_{BE}\$ mismatch, just to name a few reasons why. A lot of good work went into designing around those issues back in the 1960's. So if you are considering building these on a protoboard, you might want to research beta compensation resistors and .. well, probably Wyatt's pretty nifty design, too. (It's interesting entirely on its own.) You can also consider getting pairs of BJTs built on a common substrate for better thermal matching (BCV61 and BCV62, for example) and, in some cases, much better beta matching as well (BCM61 and BCM62, for example.)