In order for a fermentation of milk to be called yogurt (by all national yogurt associations), milk has to be fermented by S. thermophilus and L. Bulgaricus. After having those 2 required strains, any more beneficial strains is a choice.
You can ferment milk with whatever probiotics you like, if you know the correct temp and duration for those strains. It will probably have different, taste, texture etc. and it will just be considered as fermented milk not yogurt by yogurt associations standards.
That is why you probably cannot find yogurt culture without L. Bulgaricus. You can find starter without Lactobacillus acidophilus since it is not a required strain . I believe Natren has it.