Coveo does not offer grouped search results. It offers facets to drill down search results. Folding is used when you have a parent and child search results (model/variants, email thread, business/locations...) which is not your case.
Coveo is a relevance platform. Coveo believes the most relevant information will be returned in the first 3 search results, whatever its template, type or source. This, of course, requires proper indexing with the content of the documents. It can also require a few query ranking expressions (QRE) to boost the content you want to highlight if it's not returned first.
If you have your index in Coveo Cloud, you should really use Coveo Reveal Automatic Relevance Tuning (ART) feature which will automatically boost/insert search results based on previous visitors' successful searches. This basically eliminates the need to manually analyze click-through rate, click rank, queries without results and queries without clicks and manually adjust the indexing/boosting from time to time. It learns from previous visitors and improves the relevancy of search results for future visitors.
If I failed to convince you against separating the result templates and you really really need to do it, you can do it with multiple Omnibox Result List components. Each will filter the results on a specific template and ask for fewer results (e.g.: 3 each). But then, each time a user types in the search box, multiple queries will be triggered. It will perform slower, will put more load on your index (may need more resources if you are on-premises) and will use your monthly query limit faster.