The answer: No. Screen readers, etc., expect h1, h2, h3, h4, h5, and h6 to work like a table of contents for the page. A subheading, subtitle, alternative title. or tagline is not a lower-level heading. It doesn't identify any content. It's either part of the heading, or it's just content. So if the user should see/hear/etc. the sub-thing as part of the heading (i.e. if it should be visible in a table of contents) then include it inside the h* tag and then style it differently. Or if the sub-thing is too large or unimportant to appear in a table of contents, then wrap everything in a header tag, and mark the sub-thing as a paragraph... and style to taste. https://www.w3.org/TR/html52/common-idioms-without-dedicated-elements.html#subheadings-subtitles-alternative-titles-and-taglines