Could I use ThemFrame to make a magazine-style homepage that has 2 or 3 different post layouts on the same page?

For example, one full post at the top, then below that 5 full-width excerpts with thumbnails, then below that 2 rows containing 3 excerpt "tiles"?

Not yet but this is planned and coming. Currently there are 3 post container types, which you can configure & style. You can apply 1 post container type to 1 page template.

In a later version you'll be able to

• add custom post containers
• add custom page templates
• apply multiple, different post containers to the same page template

The first 2 points are coming soon, the final version with with mixing & matching may take a few weeks. It needs to be compatible with plugins and not too resource-intensive.