Hey Kristen

Thank you for posting in the Lucid Community! Unfortunately it's not currently possible to expand and collapse sections of a published/embedded org chart. However we hear you and love the idea! Would you mind adding it to our feature request form for our devs to have a look at?

As an alternative I recommend using actions and layers in your org chart to achieve the same effect as expanding/collapsing branches. Please take a look at this Community Post for more information and feel free to let me know if you have any questions. Cheers