Ummm....adjusting the K frame will make it track better as you will be aligning the front wheels with the thrust line of the car. Its got #### all to do with caster as the radius rods are attached to the front of the K frame and the lower control arm, guess where the control arm is attached? The K frame dick head. (Not directed at you Brett). So moving the K frame around will change the relationship between the front and rear wheels, and will affect where the steering wheel points, but it will not affect the caster, camber or toe-in; as every one of those angles is set by components that are bolted to the K frame only. (Unless you take into account the strut top which is bolted to the body, which is fixed and can't move anyway. The amount that it will affect the caster by moving the K frame will be minute.
There are varius types of alignments, most people will just do what they can adjust. Most modern cars it's just toe. Some have camber, very few have camber, caster and toe. With the addition of kits, you can get more adjustment out of them to COMPENSATE for road conditions, getting a car spot on to drive well on all roads is impossible. The main result of an alignment from a customers point of view is (in this order) 1: steering wheel straight, 2: driving straight, and 3: reduce tyre wear. I know not everyone prioritises the same way, but from 10 years of doing alignments, that was the general rule. A compensated alignment was the most common to get it to drive straight and have the steering wheel straight. This type of alignment aligns the front wheels with the thrust line, IE parallel to the rear wheels. Perfect in live axle cars, but pointless with IRS as the rear wheels play as much part in how the car points as the front.
There are also many factors that affect the way a car drives, not just the 3 angles that are most commonly measured. There is also king pin angle, axis inclination and included angles to take into account if the car is not driving the way it should after the alignment has been done so that the car SHOULD drive straight and not wear tyres.
To an earlier comment of ballast, yes, it does affect angles, but not so much as to adversely affect the alignment. There are a few exceptions, early Fiats is one, you have to ballast the front and rear seats to adjust them correctly. I think Audi was another one. I remember doing a Fiat by the book and it didn't drive quite right, so I set it up with just the driver in the seat and he never had a problem after that.
I could probably still tell you all the specs for Holden, Ford, Valiant and quite a few Jap cars too as I did that many of them I rarely had to look in the trusty specs book. The EH was fun as you had to remove the wheel to adjust it. Pajero's you had to jack them up to adjust them. I loved the HQ-WB as it was only two bolts and shims. Occasionally they needed a tower stretch to twist the chassis back out so you could adjust them....but I digress....