4 kW for minutes at a time shouldn't even damage it. The motor can take much more with modification, but 4 kW peak in stock configuration is a very reasonable expectation.
A hub motor in each front wheel and a middrive plus pedal output going to separate sprockets on a composite limited-slip differential in the rear. Each motor will have its own controller. I'm going to start with three Phaserunners, with 3kW/45Aphase to each front motor and 4kW/96Aphase to the middrive. Without using field weakening, this will be capable of 80+ mph @ 20S and similar acceleration to what it had with the single Leafbike @ 10kW, and with field weakening, much more top speed is possible. Possibly into the triple digits with a body.
The next body is going to make it look like a cross between an Auto Union Type C streamliner and a Stanguellini Colibri. It's going to be a slippery bastard that hopefully only needs 5 kW to cruise 100 mph.
I will later upgrade to 20kW or more with controller changeouts and wiring upgrades. Depending upon controller selection, I may go as high as 36S.
Most of the time, I will be operating it as a "street legal" ebike with a 750W / 28 mph limit to its assist while pedaling, and as a velomobile, it will be capable of much more on flat ground and downhill with just my legs making thrust. Of course, it will have a "track mode" for when no one else is looking or where jurisdiction allows me to get away with it.
I have the trike apart waiting on a piece for my front suspension to arrive. Then I can fit the front motors up to it.