Sepia toning is about as old as silver-based photography, and it still works as nicely as it did back then. In fact, it works even nicer since the advent of ‘odorless’ sepia toners based on thiourea. Apart from a more pleasant olfactory experience, these toners can be used to control the hue of the end result quite easily. Here’s how.
While cleaning up today, at the bottom of a pile of prints I found this sheet of paper I salvaged from my previous darkroom. Glued to that sheet is a series of test strips I made years ago when I was playing around with odorless sepia toner. Look:

The paper is Adox MCP312, which was still being made back then. Doesn’t really matter; the same thing can be done with any modern silver gelatin paper. What the scan above shows, is the gamut of hues that can be achieved with this sepia toner, simply by varying the ratios of the concentrates the toner is composed of.
These concentrates are made as follows (I use tap water, which is just fine, but demineralized or distilled is evidently OK too):
Stock solution A: 4% w/v thiourea. So that’s 4 grams of thiourea to a total volume of 100ml.
Stock solution B: 2% w/v sodium hydroxide, or 2 grams to a volume of 100ml.
There are some safety precautions. Handle them with care; don’t dip your fingers into these materials and then lick them off. Avoid direct skin contact, don’t get any of this in your eyes etc, and make sure that pets and kids can’t get to them either. You’ll be OK if you manage this. Let’s proceed.
The stock solutions mentioned above are for the toner. Since this is an indirect toner, you need to bleach the print first. Bleaching means converting the silver image back to a silver halide image, i.e. turning the metallic silver in the print to silver bromide, silver chloride or silver iodide. The most common way to do this is by using a regular potassium ferricyanide + potassium bromide bleach.
There are formulas out there for such a bleach, but I usually just take a pinch of both and add a little if everything goes too slow to my taste. A question that pops up often is how strong or dilute the bleach needs to be and how long the print should be bleached. The answer is: it depends. In practice, you mix your bleach, try it on a test strip and then take it from there. If it’s way too fast, dilute it a little. If it’s too slow, add the raw ingredients or concentrates if you use those.
As to the depth/extent of bleaching: you decide; you can bleach all the way to completion, or just do the highlights, or something in the middle. Try it on a test strip or print and see how it goes. Only the bleached parts of the print’s tonal scale will end up being toned. The unbleached silver will not be affected by the toner.
Back to the sepia toner. The hue variations shown above are achieved by mixing the concentrates A (thiourea) and B (hydroxide) in different ratios. To obtain the colors in the strips below, I added the following number of milliliters of concentrates A resp. B to 100ml of (tap) water:

If you do this, you’ll notice that the yellow toner (10:5) is considerably slower than the purple-brown one (1:10). The purple-brown configuration is very fast and tones a print virtually instantly; the yellow configuration can take a minute or maybe two to get the job done.
Back when I did the testing, I also made a neat little diagram, with A (4% thiourea) on the horizontal axis and B (4% sodium hydroxide) on the vertical axis; the amounts are the number of milliliters of each added to 100ml of water.

If you’re into nerdy chemistry kind of stuff, you might be wondering about the molar ratio of thiourea to hydroxide in the various settings. To save you the effort of having to calculate this, it varies from around 2:1 thiourea:hydroxide for the yellow setting to 1:10 for purple-brown.
I mentioned earlier that a potassium ferricyanide + potassium bromide bleach is the most common bleach bath for this purpose. In case you’re wondering – yes, I did in fact test some alternatives. Sadly, I did not keep the test prints, so I can’t show them – but I did keep notes.
I replaced the potassium bromide with potassium iodide. According to my notes, the effect was that the overall hue shifted towards brown for the same molar ratios. However, overall saturation/colorfulness was reduced, and the color also didn’t seem to vary quite as strongly.
Replacing the potassium bromide with sodium chloride also seemed to give less color response and reduced saturation, but the overall hue shifted towards yellow instead of brown.
Now, in hindsight, I have some doubts about the conclusion that the color response was less. I think that the molar ratios should just be adjusted and then the same yellow-brown gradation might be achievable. But maybe at reduced saturation levels compared to the original potassium bromide-based bleach.
I also tested a copper sulfate + potassium bromide bleach. This apparently gave a purple-brown image tone and bluish highlights – but my notes also mention that the prints stained considerably. It might be worthwhile to repeat this test, adding a good amount of trisodium citrate to the bleach bath. Citrate is often used in conjuction with copper sulfate, for instance in copper toner, to avoid staining. Maybe it works similarly here.
On a final note: you can buy convenient kits that contain everything you need. These kits will probably also include instructions to get different hues to the same effect as what I wrote above. However, I usually don’t bother with such kits especially if the chemistry is simple and cheap, as is the case here. For the price of a ready-made kit, you can buy the chemistry that will mix you several lifetimes’ worth of sepia toner. Besides, the ingredients can often be used for other purposes as well, and they generally keep more or less forever if stored sensibly.