This paper explores the design space of teachable social media feed experiences, aiming to empower users with agency in personalizing their feed curation. Drawing on the paradigm of interactive machine teaching (IMT), we conducted a think-aloud study with 24 users across four platforms—Instagram, Mastodon, TikTok, and Twitter—to understand the signals users use to evaluate post value. We synthesized these signals into taxonomies, which, combined with user interviews, inform five design principles for teachable feeds. These principles are then embodied into three feed designs that serve as sensitizing concepts for future research. Social media feeds are deeply personal spaces that reflect individual values and preferences. However, top-down algorithms can reduce user agency and fail to account for nuanced experiences. Users often rely on signals such as the post's author, content, and engagement metrics to determine value. These signals are nuanced and may not be captured by current preference elicitation methods like likes or dwell time. Users also express a desire for feed experiences centered around individuals they care about, better management of saved content, and more agency in curating their feeds. Prior work has shown users attempt to reclaim agency by deriving algorithmic folk theories and "teaching" algorithms to align with their preferences. However, these techniques are often unclear and may leave users feeling coerced. We propose that this is due to users' lack of opportunity to agentially articulate feedback to the algorithm. Drawing on IMT, we aim to enable teachable feed experiences by allowing users to interactively teach algorithms to align with their preferences. Our study found that users leverage a variety of signals to evaluate content, including account-related and content-related features. These evaluations are nuanced and may not be captured by current methods. We identified five design principles for teachable feeds, which are embodied in three proposed feed designs. These designs aim to empower users with agency in curating their feeds and to enable more expressive and agential feed curation. The findings highlight the need for feeds to accommodate diverse modes of browsing and to allow users to fluidly move between them. The study also shows that both people- and content-centric feed experiences can be desirable, depending on the platform and user preferences. The tension between these two approaches is evident, with users often preferring one over the other based on their goals and context. The study also highlights the importance of managing saved content and the need for more support in retrieving and curating it. Overall, the paper contributes to the design space of teachable social media feed experiences by offering cross-platform taxonomies of signals, five design principles, and three proposed feed designs.This paper explores the design space of teachable social media feed experiences, aiming to empower users with agency in personalizing their feed curation. Drawing on the paradigm of interactive machine teaching (IMT), we conducted a think-aloud study with 24 users across four platforms—Instagram, Mastodon, TikTok, and Twitter—to understand the signals users use to evaluate post value. We synthesized these signals into taxonomies, which, combined with user interviews, inform five design principles for teachable feeds. These principles are then embodied into three feed designs that serve as sensitizing concepts for future research. Social media feeds are deeply personal spaces that reflect individual values and preferences. However, top-down algorithms can reduce user agency and fail to account for nuanced experiences. Users often rely on signals such as the post's author, content, and engagement metrics to determine value. These signals are nuanced and may not be captured by current preference elicitation methods like likes or dwell time. Users also express a desire for feed experiences centered around individuals they care about, better management of saved content, and more agency in curating their feeds. Prior work has shown users attempt to reclaim agency by deriving algorithmic folk theories and "teaching" algorithms to align with their preferences. However, these techniques are often unclear and may leave users feeling coerced. We propose that this is due to users' lack of opportunity to agentially articulate feedback to the algorithm. Drawing on IMT, we aim to enable teachable feed experiences by allowing users to interactively teach algorithms to align with their preferences. Our study found that users leverage a variety of signals to evaluate content, including account-related and content-related features. These evaluations are nuanced and may not be captured by current methods. We identified five design principles for teachable feeds, which are embodied in three proposed feed designs. These designs aim to empower users with agency in curating their feeds and to enable more expressive and agential feed curation. The findings highlight the need for feeds to accommodate diverse modes of browsing and to allow users to fluidly move between them. The study also shows that both people- and content-centric feed experiences can be desirable, depending on the platform and user preferences. The tension between these two approaches is evident, with users often preferring one over the other based on their goals and context. The study also highlights the importance of managing saved content and the need for more support in retrieving and curating it. Overall, the paper contributes to the design space of teachable social media feed experiences by offering cross-platform taxonomies of signals, five design principles, and three proposed feed designs.