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

The ["How do I search?" help page][1] 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**.

<sup>(Emphasis added)</sup>

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**][2].


----------
**Example on the main site**:

 1. [Searching for `[winzip] title:folder make`][3] gives 3 results (currently).
 2. [Searching for `[winzip] title:folder automate`][4]  gives 1 result
 3. [Searching for `[winzip] title:folder make or automate`][5] **gives no results, when it *should* give at least 3 (fail)**.
 4. [`[winzip] title:folder (make or automate)`][6], etc., also fail.

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

<br>

----------
###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_id`s for the final (net) results

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

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


  [1]: https://stackoverflow.com/help/searching
  [2]: https://meta.stackexchange.com/questions/158815/please-allow-using-nested-expressions-when-filtering-with-tags
  [3]: https://stackoverflow.com/search?q=%5Bwinzip%5D%20title%3Afolder%20make
  [4]: https://stackoverflow.com/search?q=%5Bwinzip%5D%20title%3Afolder%20automate
  [5]: https://stackoverflow.com/search?q=%5Bwinzip%5D%20title%3Afolder%20make%20or%20automate
  [6]: https://stackoverflow.com/search?q=%5Bwinzip%5D%20title%3Afolder%20%28make%20or%20automate%29
  [7]: https://api.stackexchange.com/docs/advanced-search#order=desc&sort=activity&q=title%3Afolder%20make&tagged=winzip&filter=!C(o*Un*wUzi0Ii8GQ&site=stackoverflow&run=true
  [8]: https://api.stackexchange.com/docs/advanced-search#order=desc&sort=activity&q=title%3Afolder%20automate&tagged=winzip&filter=!C(o*Un*wUzi0Ii8GQ&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(o*Un*wUzi0Ii8GQ&site=stackoverflow&run=true
  [10]: https://api.stackexchange.com/docs/advanced-search#order=desc&sort=activity&q=title%3Ahttp%20class&tagged=java&filter=!C(o*Un*wUzi0Ii8GQ&site=stackoverflow&run=true
  [11]: https://api.stackexchange.com/docs/advanced-search#order=desc&sort=activity&q=title%3Ahttp%20foo&tagged=java&filter=!C(o*Un*wUzi0Ii8GQ&site=stackoverflow&run=true
  [12]: https://data.stackexchange.com/help