Op-amp can add more than two voltages, while discrete transistors can't?

A transistor can add n input signals, a crude example is the following

^{simulate this circuit – Schematic created using CircuitLab}

You can also do it with a common base circuit.

the only circuit with discrete transistors that can add two signals is the differential amplifier with the second input signal reversed before passed to the differential amplifier.

That's simply not true.

My question is, how does the op-amp add more than two input signals when it is actually made of discrete transistors circuits?

Well, a) above statement is false, b) the opamp is a differential amplifier (with a very high gain).

How the summing amplifier built from an opamp works is explained in 1000 places on the internet, so I'll allow you to research that yourself.

The short answer is that an opamp has way more going on inside than just the input differential pair. If you recreate the rest of the opamp's internal functions with discrete transistor circuits, you will get the same results.