Limit visibility on documents

Using the API, Considering the following envelope with two signers, S1 and S2 and three documents D1, D2, D3:

For D1: Contains tags for S1 and S2.
For D2: Contains tags for S1 only.
For D3: Contains tags for S2 only.

I have a requirement where S1 is allowed to see only D1 and D2 while signing. S2 can see D1, D2 and D3. It looks like the Document Visibility feature is the way to go, but S2 wouldn't see D2 because he has no tags on that document. Is there a way to do this?

Yes, Document Visibility is the way to achieve this -- but, as you point out, S2 will need to have at least one tag on D2 in order for it to be visible. To meet this requirement (while not requiring any input from S2 on D2), you might consider implementing the following approach:

Add a FullName or DateSigned tag for S2 (signer 2) on D2 (document 2). (DocuSign will automatically populate data for FullName or DateSigned tag, so no input will be required from S2 for that tag.)
To make that tag invisible, set its Font Color property such that it matches the background color of the page. For example, if D2 has a white background, set Font Color of the S2 tag to White. This effectively makes the tag invisible, but it still technically exists on D2 and belongs to S2, so D2 will be visible to S2 when using "Document Visibility" feature.

Note: Keep in mind that the "hidden" FullName or DateSigned tag will cover up whatever space it takes up in your document once DocuSign auto-populates it with the appropriate value -- so be sure to place it somewhere that it doesn't inadvertently 'white-out' (cover up) content in the document.