Most airliners have a 3-segment climb. The J31 had a special certification which included a 4th segment, which was from the lift off to the point the gear was retracted. The reason that was done was because the plane wouldn't necessarily climb on one with the gear out.
Now, that being said, I believe I conveyed some incorrect thoughts in another post.
There are really three scenarios for a continued takeoff: 1) A successful takeoff; 2) An engine failure at V1 - the certification and training scenario; and 3) engine loss after V1
In all instances, OEI performance is considered and we set the aircraft up for a "V1 cut". Trims, the three degrees per second rotation and target takeoff pitch are all predicated on the perfect engine failure scenario, giving that three-degree-per-second rotation into V2.
An All-engines takeoff after you rotate, you will exceed V2. Some operators may want you to pitch to that number. However, once you pass V1 with all engines running you have excess energy at that point. In this scenario, my aircraft will capture a speed up to V2+25. Other aircraft may have different logic, or the speed bug might stay put (Of course, referring to aircraft with flight directors and various vertical modes)
For the third scenario, all engines operating into an engine loss after V1. The aircraft will have far more energy than an engine loss at V1. In this instance, the aircraft should be flown between V2 and v2+10. If you are above V2+10, as far as my knowledge goes, you should convert some of that energy and fly to V2+10.
Finally, in the V1 cut scenario, the aviation gods have aligned and a theoretical event actually happens. At that point, you're going flying. Due to the energy state of the aircraft, a nominal rotation should set you into your target speed right about V2. There shouldn't be excess energy to bleed at that point.
V2 is like Vref. It's a -0/+X speed. You should never be below it.
In any instance, VFR/VMC/IFR/IMC or if you're covered in green slime, you fly that engine out profile. An emergency that you have trained for and are set up for really shouldn't be a time to invent.
This brings around aborts.
Most operators I know of, and indeed the two I have worked for, take a couple abort philosophies. First, is Below 80 knots. You abort for anything. Above 80 knots, you abort for major things that will keep the aircraft from flying. At V1, you fly. More advanced aircraft even have inhibitions built into the EICAS to support this idea.
Bad things typically happen for post-V1 aborts in Part 25 airplanes.