How Do Amps Affect Soundstage?

The pairing of the amp with the speakers matter more generally than the amp itself...For soundstage... ( for bad amp exist too )

But the main central factor is the pairing speakers/room if by soundstage we means not only differential imaging and the soundstaging measured apparent dimensions but also 3-D holographic volume for each instruments...

Also on par with the relation Speakers/room will be the recording itself... All recordings played on an audio system  did not give rise to a soundfield filling  all the room in front and behind the speakers and around the listener...Some recording lack lateral presence or in detph differentiation, some others put the sound more out of the speakers laterally and not in front of us too etc... i experienced all possible soundstage dimensions in my room... Thisc differ from recordings to recordings...

The choice of dac and the choice of the amp import less than the total synergy between them and with the speakers/ room acoustic... the  speakers/room acoustic pairing and coupling and the recording state of each album  being the two most impactful parameter after the synergy between amp and speakers  which is the less important factor but without it nothing will work well...

At the end not all factor impact the same but each one of them matter...Nothing impact so heavily than acoustic , but if the synergy between speakers and amp is not optimal, you will not be able to correct it with acoustic...

@mathiasmingus 

I have found that all things matter when it comes to soundstage. A better preamp, amp, integrated, speakers, room setup, and yes, even cables help. I have cheap source and middle of the road everything else and I have a huge soundstage. For me room setup and speaker setup made the biggest difference. Wife aloud me to put up some sound absorbing panels and move the speakers four feet (from the front) out into the room and bang, everything came together.

All the best.

I have heard very good sound staging with otherwise bad sound. Distortion will not always reduce the size, width, and depth of the sound stage, although it usually doesn't help. It might sometimes, for some people. I've had the soundstage pop into place with a little equalization, proper application of a house curve. For the sound stage of a 2 channel, 2 speaker system, there's abundant  interaural crosstalk that is unnatural and difficult for the ear/brain to interpret consistently. How that gets interpreted depends on a lot of factors and can make it tricky to get a good soundstage, which may happen for one person and not another listening to the same system in the same sweet spot.  Addressing interaural crosstalk means doing something beyond the orthodox 2 speaker listening triangle. My experience is that there's a hard upper limit to what can be done with just two speakers in terms of sound stage. You may find something that works really well for you. Some things that seem to always help are well matched speakers and amp channels - as close to identical as possible, perfectly level matched. Good off axis performance of the speaker can also help, and dealing with early reflections by carefully placing the speakers and judicious application of room acoustics. I think it generally helps to have a decent distance from the speaker to adjacent wall surface, which will provide some delay and attenuation of early reflections. The 2 speaker listening triangle is a delicate and fussy thing that presents the ear/brain with a signal that has inconsistencies in terms of soundstage and tone that can at best be mitigated.

Amps do affect the sound stage quite a bit.    I have found overall noise is a significant factor in soundstage width and depth.  Quieter your components usually contribute to a larger, more impressive sound stage. 

I have done my own listening test using up to 4 different Amps - using the exact same equipment, locations, music and just switching Amps.  Yes Amps can make a huge difference.  My Brystons 4BSST series produced the tightest most stable  imaging and sound stage.  They also had lightening fast response and slam thru my Maggie 3.7i.  My BAT 655SE produced deeper and better definted bass and seemed to have endless power.  In most ways the BAT are more pleasant to listen too, but they just don't hold imaging like the 4BSST.  I'm just guessing here and I'd love to know if lower frequencies maybe don't give us the same imaging clues as higher frequencies.  Maybe the BAT Amp's low frequencies emphasis drowns out the mids and highs that are more important for imaging.