Grouping multiple objects
Yes- you can connect objects together using something called parenting. 
There’s a tutorial here

https://www.surfacedstudio.com/tutorials/adobe-effects-basics-tutorial-parenting

You could also pre-comp the objects together. 

https://greyscalegorilla.com/tutorials/fun-with-precomping-in-after-effects/

Parenting is like one object controlling another (or one object controlling many other objects). Precomping is more like making a new video and placing your objects inside it (sometimes called nesting in video editors).