Why does this 500ml bottle of beer only contain half a liter? There must be a way to put one liter in, I've got to discuss this with the brewery...
Sorry for my sarcasm, but a modern AWG's output stage is quite a tricky design, usually consisting of several, stacked current feedback opamps that, depending on the selected range may or may not get used (thus the array of relays). Offset mixing is often taking place via a separate DAC and passively added to the waveform signal in order not to waste signal resolution, fidelity and to introduce distortion. On these output designs, the factor limiting the output amplitude usually isn't gain-bandwidth product of the amplifier but rather slew rate at the required drive currents.
Though the amplifiers obviously provide some headroom that could possibly be exploited, I'm very much in doubt that you will find any manufacturer of such gear who would support you in an attempt to do so. A dedicated power amplifier after the AWG's output is definitely the way to go.