Can I make a deep image with OpenEXR? I went through the OpenEXR technical introduction found here: it says that besides multi-channel files, OpenEXR also allows for the creation of "deep" files: i.e. it allows for assigning multiple recordings of a value (or a set of values) to the same channel.

I am using Blender to simulate reflection spectra. For this I loop through a parameter that takes on more than 300 different values, and for every value I use Cycles to render a new image of my scene. Instead of assigning every RGBA-output of every rendered image to a new channel, I would like to assign all 300 images to the same channel, in an ordered way. All 300 values of the parameter should be stored together (also ordered) in another channel of the multichannel EXR.
This would mean that within the same file, I would be able to look up every one of the 300 rendered images (beauty passes) by its corresponding value of the parameter. 

Is there a way to do this with Blender? I found good explanation about how to create multichannel EXR, but nothing on how to make a channel in such a multichannel file "deep". I tried connecting many input nodes to the same output channel but this isn't possible.
Blender is not the right tool to do this. You can do almost everything in Blender, but sometimes coding and doing it yourself is required.

You cannot obtain the deep image directly, because there is no renderer (as my knowledge goes) that can output that (a volumetric output).

You get multi-channel output at most (beauty pass, z-depth, shadow pass,..) - and this is what most 3d apps will let you save:

Save all render passes to a single EXR image

Some will let you save this as deep image, for example MentalRay.

To get your image with deep pixels, you would have to create it from all the rendered images. To be able to do this inside Blender, you would have to use the OpenEXR source code and code it yourself and run it from Blender through python bindings. Some compositing applications offer creation of openEXR deep images, like Nuke for example.

A deep image is nothing else than volumetric data structure in camera space. You cannot 'render' such data in Blender, but you can create them (smoke, fire, ..) and export as Alembic (in global space). From there it might be easier to handle such data externally.

If you need to convert particles or geometry into volumetric data structures, Houdini is a good tool to do that.