Can I boost/penalize certain objects in the search results?

Definitely!

An easy way to do that is to have an attribute that you will use to separate the featured products from the others.

[
  {
    "name": "Banana",
    "featured": true
  },
  {
    "name": "Apple",
    "featured": false
  }
]<br>

Add this attribute (e.g. feature = true/false) in your records, and use it at the top of the setting Custom Ranking.

That’s it! The objects that are tagged “featured” will now have a bonus in the rankings.

You can also use the same method with more than 2 levels of featuring. For example, instead of having a boolean value for your attribute featured, you could use an integer with values ranging from 0 to 10, which would define 10 different levels of promotion.

We’ve decided to use this approach based on attributes, instead of using a more common coefficient based approach, because it offers a better consistency/control, and in the end a better relevance.