You can create a Customer Match Audience and Use the same audience in your Campaigns to only those people whose behavior is similar to your existing customers. Once you have prepared the audience, you can use the audience for any kind of Campaign that is supported by Google, like Search Campaign, Shopping Campaign, Display Campaign, and YouTube Campaigns.

Brand Search Campaigns are normally meant to retarget people who are searching for your company. You can create a list of customers who have purchased more than 3 times from your store and block those customers from seeing your ads as they are more likely to click on your Organic Rankings and place an order. 

1 – You can create a new shopping campaign with the entire catalog exclusively for those who have already purchased from your store with higher or same bids and high priority. The budget of This campaign can be kept in such a way that it keeps getting impressions throughout the day. 
2 – You can create a cross-sell campaign of accessories for the customers who have purchased the main product.  

For example, if you are doing An Event in a particular region or state, you can create an audience of customers who have purchased from your store from that particular region and run a Display or YouTube campaign to spread awareness of The Event. 

There are many other ways to use the audience if you have sufficient audience size for a particular campaign type, you can improve the precision of targeting of a campaign.