I am aware that the essential subject has already been discussed but after a variety of recent observations for my TOS Enterprise WIP and a suggestion of a friend I won't exclude the possibility that we might be looking at a minimum of a) three engine rooms in the b) "engineering section" of the c) engineering hull.
In TOS there is a variety of episodes that are outspoken clear about the warp engines or nacelles containing antimatter and matter-antimatter reactors and blssdwlf has not only compiled these canonical dialogue statements but also drawn some fascinating conclusions (three matter-antimatter reactors) he posted and illustrated in his thread: http://www.trekbbs.com/showthread.php?t=119751&page=16
(I recommend starting at post # 229).
I believe the dilithium re-amplifying room from The Alternative Factor to be separate place where you take exhausted crystals from the dilithium crystal ‘cage’ in the middle of the double-triangle casing in the (warp) engine room for “re-amplification”. To power the warp drive (and else) they have to be placed back in their cage(s) for performance.

As it appears the cage can only hold one crystal at a time and I presume the matter-antimatter annihilation energy from the nacelles’ reactors (in addition to the TOS “warp core” suggested by That Which Survives) is also routed through two crystals easily accessible for replacement by the engineering personnel and located somewhere in the engineering hull.
The very TOS beginning and Mudd’s Women suggested that all three matter-antimatter reactors of the Enterprise were working at full power chasing Mudd’s ship through an asteroid field resulting in the subsequent burnout of (di)lithium circuits and subsequent shutdowns of the reactors:
CREWMAN [OC]: This is the Engine room. Temperatures are passing the danger line.
FARRELL Our deflector screen's weakening, sir. We can't protect them much longer. (lights flicker)
SULU: That was one of our lithium crystal circuits, sir.
KIRK: Bridge to transporter room. If you don't start beaming that crew over soon
SCOTT [OC]: They're not answering our signal. There's nothing to lock onto.
SULU (lights go out again) Another circuit, sir.
...
SULU: Another lithium circuit. Now supplementing with battery power, sir.
At this time they appear to have only had three dilithium crystals circuits onboard (and no shuttlecraft
).
If the structure in the engineering section only holds one dilithium crystal circuit, where is the location of the other two as it is unlikely they exchanged dilithium crystal circuits during the chase (!)?
My friend wondered if the shaking and G-Force pressure seen in The Doomsday Machine might be an indicator of engine room orientation aboard the Constellation but I attributed the erratic movement of Scotty to hickups of the damaged inertial dampers and/or unfamiliarity of the director with the Enterprise’s deck layout, which IMHO could look like this: https://www.dropbox.com/s/yscj4a4hid0p2v7/USS%20Enterprise%20Engineering%20Deck%209%20Uncompressed.jpg
However, with The Immunity Syndrome I feel that’s a more complicated story. We had already seen in an earlier episode produced (Mirror, Mirror) a rectangular console in the Emergency Manual Monitor (EMM) on the upper level of the (warp) engine room, yet for The Immunity Syndrome they decided a) to remove the rectangular console and b) to put the semi-circular console from the Auxilary Control Room in its place instead - to suggest this is a different engine room?!

In the scene from this episode, when they combine warp and impulse power for one major forward thrust, we see accordingly on the bridge that they are all being pressed into their seats and towards the stern of the ship.

However, in the engine room that’s a totally different story. To the left side of 'this' engine room would be the entry and to the right side the ‘cathedral’ with its tubes (studio set).
Thus the shot of the warp engine room seen from this “EMM” clearly suggests that the bow of the ship is to the right and the stern is to the left which would make this another engine room with a dilithium crystal cage as it apparently can’t be the (main) warp engine room in the center of the engineering hull.

Now, do we have to consider the existence of one starboard warp engine room, one to the port and one in the center? I doubt there'd be enough space.
Bob
In TOS there is a variety of episodes that are outspoken clear about the warp engines or nacelles containing antimatter and matter-antimatter reactors and blssdwlf has not only compiled these canonical dialogue statements but also drawn some fascinating conclusions (three matter-antimatter reactors) he posted and illustrated in his thread: http://www.trekbbs.com/showthread.php?t=119751&page=16
(I recommend starting at post # 229).
I believe the dilithium re-amplifying room from The Alternative Factor to be separate place where you take exhausted crystals from the dilithium crystal ‘cage’ in the middle of the double-triangle casing in the (warp) engine room for “re-amplification”. To power the warp drive (and else) they have to be placed back in their cage(s) for performance.

As it appears the cage can only hold one crystal at a time and I presume the matter-antimatter annihilation energy from the nacelles’ reactors (in addition to the TOS “warp core” suggested by That Which Survives) is also routed through two crystals easily accessible for replacement by the engineering personnel and located somewhere in the engineering hull.
The very TOS beginning and Mudd’s Women suggested that all three matter-antimatter reactors of the Enterprise were working at full power chasing Mudd’s ship through an asteroid field resulting in the subsequent burnout of (di)lithium circuits and subsequent shutdowns of the reactors:
CREWMAN [OC]: This is the Engine room. Temperatures are passing the danger line.
FARRELL Our deflector screen's weakening, sir. We can't protect them much longer. (lights flicker)
SULU: That was one of our lithium crystal circuits, sir.
KIRK: Bridge to transporter room. If you don't start beaming that crew over soon
SCOTT [OC]: They're not answering our signal. There's nothing to lock onto.
SULU (lights go out again) Another circuit, sir.
...
SULU: Another lithium circuit. Now supplementing with battery power, sir.
At this time they appear to have only had three dilithium crystals circuits onboard (and no shuttlecraft

If the structure in the engineering section only holds one dilithium crystal circuit, where is the location of the other two as it is unlikely they exchanged dilithium crystal circuits during the chase (!)?
My friend wondered if the shaking and G-Force pressure seen in The Doomsday Machine might be an indicator of engine room orientation aboard the Constellation but I attributed the erratic movement of Scotty to hickups of the damaged inertial dampers and/or unfamiliarity of the director with the Enterprise’s deck layout, which IMHO could look like this: https://www.dropbox.com/s/yscj4a4hid0p2v7/USS%20Enterprise%20Engineering%20Deck%209%20Uncompressed.jpg
However, with The Immunity Syndrome I feel that’s a more complicated story. We had already seen in an earlier episode produced (Mirror, Mirror) a rectangular console in the Emergency Manual Monitor (EMM) on the upper level of the (warp) engine room, yet for The Immunity Syndrome they decided a) to remove the rectangular console and b) to put the semi-circular console from the Auxilary Control Room in its place instead - to suggest this is a different engine room?!

In the scene from this episode, when they combine warp and impulse power for one major forward thrust, we see accordingly on the bridge that they are all being pressed into their seats and towards the stern of the ship.

However, in the engine room that’s a totally different story. To the left side of 'this' engine room would be the entry and to the right side the ‘cathedral’ with its tubes (studio set).
Thus the shot of the warp engine room seen from this “EMM” clearly suggests that the bow of the ship is to the right and the stern is to the left which would make this another engine room with a dilithium crystal cage as it apparently can’t be the (main) warp engine room in the center of the engineering hull.

Now, do we have to consider the existence of one starboard warp engine room, one to the port and one in the center? I doubt there'd be enough space.
Bob