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The API currently does not support this, but then neither does the website itself.

The "How do I search?" help page says:

OR operator

To combine results from multiple tags, separate the tag names (enclosed in square brackets) with the word "or": [widgets] or [geegaws] returns questions tagged with either tag.

^{(Emphasis added)}

Note that it only refers to tags in conjunction with the or operator. No facility is made for general or operation.

Here's a related feature request which you can/should upvote.

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Example on the main site:

1. Searching for [winzip] title:folder make gives 3 results (currently).
2. Searching for [winzip] title:folder automate gives 1 result
3. Searching for [winzip] title:folder make or automate gives no results, when it should give at least 3 (fail).
4. [winzip] title:folder (make or automate), etc., also fail.

The API equivalents ([one][7], [two][8], [three][9]) give the same results.

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###Workarounds:

The Most timely/accurate workaround is: for each of the optional terms, search separately and then combine the results (stripping duplicate matches).

For example:

1. Suppose your keywords were: class and foo.
2. [Search for title:http class][10] (only 3303 results, currently).
3. [Search for title:http foo][11] (81 results).
4. Repeat for each additional keyword.
5. So we have 3384 gross results, then remove any duplicate question_ids for the final (net) results

This is annoying and inefficient, but it works and is easy to automate.

Other possible workarounds include using a [SEDE][12] query or Google search with the `site:` parameter.

[7]: https://api.stackexchange.com/docs/advanced-search#order=desc&sort=activity&q=title%3Afolder%20make&tagged=winzip&filter=!C(oUnwUzi0Ii8GQ&site=stackoverflow&run=true [8]: https://api.stackexchange.com/docs/advanced-search#order=desc&sort=activity&q=title%3Afolder%20automate&tagged=winzip&filter=!C(oUnwUzi0Ii8GQ&site=stackoverflow&run=true [9]: https://api.stackexchange.com/docs/advanced-search#order=desc&sort=activity&q=title%3Afolder%20make%20or%20automate&tagged=winzip&filter=!C(oUnwUzi0Ii8GQ&site=stackoverflow&run=true [10]: https://api.stackexchange.com/docs/advanced-search#order=desc&sort=activity&q=title%3Ahttp%20class&tagged=java&filter=!C(oUnwUzi0Ii8GQ&site=stackoverflow&run=true [11]: https://api.stackexchange.com/docs/advanced-search#order=desc&sort=activity&q=title%3Ahttp%20foo&tagged=java&filter=!C(oUnwUzi0Ii8GQ&site=stackoverflow&run=true [12]: https://data.stackexchange.com/help