So you just powder your soap (or turn your soap to liquid) and use nothing else for laundry soap?
The reason I'm asking these questions is because you said you prefer soda to borax and I'm trying to decide how I want to proceed with trying to use soap for laundry detergent AND if I can use my alkenet colored soap.
Adding some alkali (but it's got to be more alkaline than baking soda) will make it a little stronger and a little cheaper. But if I had to choose between some of the recipes I've seen going around in recent years that are more alkali than soap, and using nothing but soap, I would easily choose using nothing but soap for laundry.
Lately in cx with this discussion I've been doing some Googling for state-of-art soap-based formulas for laundry detergent, and they're typically 70-80% soap, 5-15% alkali (carbonate or silicate of soda), and the rest other stuff. That's not out of line with what would've been said over a century ago.
In water that was "hard" enough to make a big difference, it never paid to add enough carbonate to wash water to take up all the calcium, etc. unless it was done separately. Laundries would "soften" their water separately rather than doctor the soap. Consider this:
Na2CO3 + Ca(OH)2 --> CaCO3 + 2 NaOH
Meaning that if all the "hardness" in the was water to begin with was lime (it's not, but that's not too bad an approximation), you're adding washing soda to turn it into chalk and lye -- neither of which are good for fabrics. So typically soda-"built" soaps would have only enough carbonate in them to boost the alkalinity of the wash water a little, regardless of whether it was anticipated there'd be more calcium in the water that could react with more soap and/or carbonate. It did the clothes more of a favor to generate scummy lime soap in the wash water than to try to precipitate all the calcium as chalk, if there was a lot of it.
Silicates were better additives than carbonate or borate, and the only reason I imagine they're not used in the home recipes is that alkaline sodium silicate is not a common grocery item. It is a little more hazardous to work with than washing soda would be, although soaps made with the amounts of sodium silicate typically used are no more hazardous than plain soap powder.
I might recommend sodium citrate as a water conditioner for these recipes, except that I read once that citrate's affinity for Ca++ isn't high enough to efficiently pull it away from soap, so you'd have to use a lot of it. Trisodium citrate's not so strongly alkaline so it wouldn't do clothes any harm, and it complexes calcium without making a chalky residue so it's advantageous there, but apparently you'd need a lot of it, which would cost you, to make a difference in "hard" water.
If you can get sodium hexametaphosphate (the original Calgon), that'd be even better as a water "softener". It's still used in non-alkaline bath salts for that purpose, but has become somewhat expensive. You can use enough of it to fully "soften" the wash water and it does clothes (and skin) no harm at all. However, if you wanted to optimize your laundry soap, it'd still pay to put in a pinch of sodium silicate or even carbonate even if there's also enough phosphate in there to complex all the "hardness" cations. If all the people in the world who used home recipes for laundry were to switch to phosphates for their soap "builder", the pollution impact would be insignificant because so that's so few people compared to those using no-phosphate commercial detergents (and their toilets).