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Let's say that the ISS has to be immediately evacuated and that one of the two Soyuz is broken.

Could the crew quickly remove "unnecessary weight" (seats maybe?) and fit six person to return back to Earth?

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No. And it doesn't even matter that there's no space for a crew of six no matter how small they might be or if they threw away some other pieces and try to make do. The life support of the descent module of the Soyuz TMA can only support up to three people. Since descent time is more or less constant regardless of the descent mode, and there's no way to descent faster after module separation without killing the crew in the process, you could only transport additional crew of three if they don't depend on module's available life support's provisions. I.e. if they're already dead and essentially cargo.

They wouldn't fit anyway, Soyuz TMA descent module can fit 50 kg of cargo for a crew of three or 150 kg for a crew of two, with total capacity of 305 kg. And with habitable volume of only 3.5 cubic meters, it gets pretty tight in there with all the essential equipment, spare chute and astronauts / cosmonauts in their Sokol IVA suits as it is:

   enter image description here

   ISS crew members, U.S. astronaut Daniel Burbank and Russian cosmonauts Anton Shkaplerov and Anatoly Ivanishin,
   crowded inside their Soyuz capsule shortly after landing in Kazakhstan, on April 27, 2012. (Reuters/Sergei Remezov)

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    $\begingroup$ But there are some margins to use. Better than casting lots, drawing straws and arguing about who is to have a chance to survive. They could skip the pressure suites to make room, they are only needed if something goes wrong anyway, right? $\endgroup$ – LocalFluff Dec 10 '15 at 16:11
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    $\begingroup$ @LocalFluff If cramming six people into a Soyuz means all six will definitely die from asphyxiation, that would not be better than drawing straws. I could see it bearing some discussion and maybe jerry-rigging a way to add maybe one more additional person if there's room for some kind of auxilliary oxygen. Better to brainstorm ways to keep the other three alive on the ISS long enough for another Soyuz to arrive, if it really came down to it. $\endgroup$ – Todd Wilcox Dec 10 '15 at 17:59
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    $\begingroup$ I wonder if getting rid of the spare chute would allow for cramming one extra. Definitely not three, because you'll go over weight limit, and with the 6g without proper safety belts and extra seat it would be bound to end up with some broken bones, but might be survivable. $\endgroup$ – SF. Dec 10 '15 at 21:59
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    $\begingroup$ Our Russian colleagues are super focused on getting a Soyuz seat pan customized for each person. It was a huge deal and some really experienced specialists were involved. From the level of effort devoted to this, I gathered that if you didn't land in your custom fitted seat you were going to be seriously injured. space.io9.com/… $\endgroup$ – Organic Marble Dec 11 '15 at 1:36
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    $\begingroup$ Yep, what I assumed, some broken bones would be a given. Possibly worse injuries too. Definitely not a landing one could walk away from on their own (and probably all of the astronauts would get injured, not just the "extra".) $\endgroup$ – SF. Dec 11 '15 at 2:46
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I found an actual reference for this, although it's in a memoir, not a technical book. Jerry Linenger's book Off The Planet states

Unfortunately there is no way to squeeze more than three people into a Soyuz capsule. There are only three seats in the spacecraft. Even if one other person, without a seat, sprawled across the sitting crew, the presence of that fourth person would shift the center of gravity of the vehicle, most likely causing the capsule to tumble during reentry. A tumbling vehicle means that the capsule's heat shield would not be pointed in the proper direction.

Page 112 of the McGraw-Hill 2000 printing.

This was in reference to the fire emergency on Mir during the Mir 22-23 crew handover period. There were two Soyuzes docked and six people on board. The fire blocked access to one of the Soyuzes. Linenger concludes that it would have been impossible for all six to evacuate in the accessible Soyuz.

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According to the NASA fact sheet on Soyuz landing, it takes about 3.5 hours from undocking to a landing on Earth. But in the three first hours they have the otbital module, and you can likely then cram up to six people into Soyuz.

Mass limit
The Soyuz has a cargo capacity of 50 kg in addition to three crew members. If you dropped the Sokol suits, which are only a backup system, you can fit in one more without going over limit. But how the mass is distributed is also important, as the capsule has to be balanced

Volume
As for volume, it is pretty tight though. Is it enough space to fit one more person in the descent module? Finding pictures which clearly shows the spare room is difficult, so I decided to do some original research. As it turns out, crowding a 3.5 cube meter room with four people is not all that difficult. The spare room of the capsule is also pretty much concentrated between the commander and the hatch.

Life support
Surviving in a closed space is always a question of CO2 removal. Assuming worst case, that the system can only support three people, carbon dioxide from the forth crewman will build up in the atmosphere of the capsule. At normal human carbon dioxide emission, the concentration after half an hour would be between 0.5 and 1 %. That is still within acceptable limits. Using the equation found here, I get a comparable ressult.

Acceleration
The Soyuz has custom fit seats for the Cosmonaut, and that indicates high acceleration is a big deal. But like @SF said, they are likely to get away with it with only broken bones or minor damages.

In conclusion, it is not possible to land the Soyuz safely with a six person crew, but it may be possible to fit in one more.

This is not to say that the Soyuz can actually carry four people, but it may be possible in theory. Real world safety procedures will never allow this as it has a too high risk.
Even emergency events have never been enough for trying to stretch the capacity of the spacecraft.

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  • $\begingroup$ I am not sure this adds anything not already present in the existing answer and comments. $\endgroup$ – James Jenkins Dec 14 '15 at 13:43
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    $\begingroup$ @James Jenkins It adds a little bit about the carbon dioxide issue, and also in contrast to TildalWave's answer claim that managing a four person descent might be possible. $\endgroup$ – SE - stop firing the good guys Dec 14 '15 at 16:13
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    $\begingroup$ You have 3.5 cubic meters of air space, with one additional person. For simplicity lets say you put one person all alone in the space with no CO2 scrubbing. If I read this kimberlymoynahan.com/2012/04/… correctly and do the conversion right the levels get toxic in about 2 hours. If you have good reason that the CO2 is not going to be a problem you should add it to you answer with references. Note this is a 3.5 hour trip, not 30 minutes $\endgroup$ – James Jenkins Dec 14 '15 at 16:22
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    $\begingroup$ The 3.5h figure could be shortened. It would be possible to do the deorbit burn closer to the station (possibly damaging it). Earth is only one hour away from deorbit burn to landing. $\endgroup$ – Antzi Dec 30 '15 at 12:38
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    $\begingroup$ The white bags with the orange straps contain survival equipment, in case they land somewhere unexpected. This could be removed and create more space, but complicating the balance issue. $\endgroup$ – Innovine May 11 '19 at 7:21

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