Well your answer is partially contained in your question – Acrylic ink extender ! can be used to get a lighter shade of the original colour & obviously make the original bottle of ink last longer. Extender costs around the same as the ink does , so little or no money saving in using extender.

A high quality acrylic ink suck as Daley Rowney FW can be diluted 1 part ink to two parts water & still dry waterproof OK.- but again you will have a lighter tone of colour .

Assuming you are using dip pens to apply it, different models & makes of dip pens run wetter or dryer & are therefore delivering different amounts of pigment – So much so that for a larger wet nib making a broad line, I use the FW ink diluted as above to leave the same tone as the pure ink through a fine mapping pen used lightly on a single drawing !
Another thing to bear in mind is that if you do add water 2:1 to the ink you will not be able to flare the dip pen lines as broadly as when the ink was untouched – everything depends on your personal needs for the project.

It would help if I had a clearer idea of exactly what you intend doing but I can tell you that acrylic mediums sold for use with paint are useless with ink intended to go though a dip pen (even the thin stuff) – It MUST be an acrylic INK extender.

Hope some of that is helpful , I can only report my own experiences with acrylic ink through a dip pen although when I tried using it through a brush in a wash recently I did notice that it appeared to require even further dilution for a given tone.

Too much water or extender & you lose the waterproof qualities of the acrylic ink & also potentially leave so little pigment that it would be prone to fading fast when exposed to light, so try to start out with a tone which is pretty near(ish) to your target tone. ie. light grey from a black might be pushing it to far.

Experimentation specific to your techniques exact requirements is the way ahead of course , I normally use a syringe & an empty ink bottle & mix small amounts , keeping a very careful record of the mix so I can repeat it when I find the perfect mix/tone/waterproofness balance.
Cheers Mike