Not with BP-Default, you could add the functionality to your own theme.
There isn’t a custom profile plugin at the moment. There exists a group css plugin that could be used as an example in creating your own plugin. https://wordpress.org/extend/plugins/buddypress-group-css
Another option is adding profile fields and then mapping that info to CSS. See this forum topic: https://buddypress.org/community/groups/how-to-and-troubleshooting/forum/topic/css-for-member-page
oh and you could use theme switcher plugins to change a site wide theme to predefines styles. Create little thumbnails like twitter and when user clicks image it switches to that theme/style.
True there is that background image plugin but the question was “theme like twitter” and so far nothing like that exists for profiles
@nahummadrid I hope there is going to be an upgrade, because currently on buddypress 1.5 it’s not working.