The way Instagram works, it figures out who you’re associated with, and it shows your posts to their network and vice versa. There’s a few ways to “partner” with bigger accounts.
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Be active and tale part in liking and commenting on others. Post regularly and schedule your posts. Compose attractive and fun captions. Find your niche and be focused on that field. Complete your biography and use a few (related) hashtags there, too. Use popular hashtags.