Making Sweet/Enriched Breads Out of Sourdough Starter

I doubt it's possible to make sourdough bread with no hint of acidity. But to minimize it maintain your starter warm, and use it right at peak time, don't let it fall. A few consecutive feeds should help a lot. Maybe one small feed in the afternoon, bigger feed overnight, and a small feed in the morning before mixing the dough.

Providing more detail about your process can help get more specific and better advice.

Are you talking about tea breads (for lack of a better word) like banana bread or cranberry orange bread? Or are you talking about a gluten-crumbed bread that is sweet but meant for toast or sandwiches? Or even a brioche or challah-like bread?

Starters can be maintained in such a way that the sourness is almost absent  but it has to have some lactobacillus or the thing would go moldy. Maintain it to skew it towards yeast. All that info is available here-a and has been discussed in great detail numerous times over the years. Search box is your friend.

I'm not the one to ask exactly how as I routinely neglect my starter or maintain it erratically. Though I do say that my starter generally produces non-sour loaves of all kinds. I often use a 100% preferment of some kind and feed my long-stored & refrigerated starter few times before using.

I use discard in my banana breads,pancakes and muffins. No recipes. On those I often fly by the seat of my pants.

Have fun. More info needed in order to answer your questions.

A couple of things that I know about that can reduce the acid of a lEvian in addition to what the others have already posted.  Make the levain a white flour non whole grain levain.  Whole grain levain will generally have a greater acid load than white flour starters.  Reduce the hydration of your levian, the higher the hydration in general will allow a greater acid load to develop than a lower hydration levain.

Benny

It’s definitely possible to make naturally-leavened bread without a sour flavor. The more enriched the dough is, this can be a more challenging thing..

Echoing what others have said here:

1. White flour only

2. More frequent refreshes

3. “sweet starter” - if you don’t want to go the full multi-stage “lievito madre” mode, you could borrow from Ian Lowe and his single build sweet starter idea. This is 100% flour, 100% water, 50% starter, 22.5% sugar. 

I believe the thinking behind this is two fold (Ian could tell you much much more about this): To “spread out” the osmotic stressor (sugar) in multiple builds so it’s not all landing on the final build. And also that the bacteria in the culture are more susceptible to osmotic stressors, and from using this method, you could end up with a more yeast-heavy mix of organisms (less sour). 

As a final note, unless you are a naturally-leavened purist, (which is a fine aspiration to have, although I do not share it) I think it’s more than fine to add some baker’s yeast to a naturally-leavened enriched bread. Especially if you’re worried that the levain alone may not be enough to leaven the bread with all the fat and sugar. 

Hope that helps!