Operation Amplifier with Transistor output
What you can try is this: Connect a push-pull transistor pair to the output of an opamp and connect the feedback path to the output of the push-pull pair instead of the opamp's output. This way, you have the opamp do all the voltage amplification, and you can use the transistors for additional current amplification. The trainsistor pair's non-linearity will be compensated by the opamp because it's inside of the feedback loop.

This is an example I found after a quick search illustrating the general idea.

This application note (pdf), almost certainly written by Jim Williams (note the screenshots of his Tek 556 scope!), shows some practical schematics. Figure 3 details a circuit that does not meet the question's requirement of 100 MHz, but is capable of doing at least 10 MHz. The text says it is limited mainly by the OpAmp, and not by the discrete booster stage. It would be interesting to see what the circuit does with a faster, more modern OpAmp... Not perfect, but maybe close to what your question asks for!

Here's a later app'note (pdf), also by Jim Williams, featuring circuits with a -3&nbsp;dB bandwidth beyond 100 MHz. A very good read!