CORE allows you to set up budget templates in general and then assign them to multiple projects from the Settings > Projects > Budgets screen. You can also create unique, project-specific budgets in the Projects screen.
In case of 'template budgets' in CORE, you can add all the budget details that your team uses most of the time and add line items for all the common activities and expenses involved. In the future, you can create budget templates using the Create From Existing Template option, choose this template budget to copy from, and then assign it to the relevant projects. Check CORE Help Center for details.
After logging time and expenses against such projects, you can run the Budget Comparison reports to track their progress.
In case of project-specific budgets, you can go into the project details and create a unique budget for it so that it is not shared with any other project. Check CORE Help Center for details.