A cross-functional team is a group of people with different functional expertise working toward a common mission and goal. It may include people from finance, marketing, operations, and human resources departments. It may include employees from all levels of an organization (Intra) and may also include people from outside (Inter) an organization (in particular, from suppliers, key customers, or consultants).They are sometimes placed on a Working Group to solve a particular problem. 
Intra-Cross Functional Teams
These teams are good at bringing in other departments, as in a Matrix Organization, that have a role in the Acquisition Process to seek their commitment to improving the purchasing process. They help solve problems within the organization before they arise and foster communication to improve efficiency. An example would be getting better defined requirements from the engineering department with regards to a new tool that needs to be purchased. These better requirements would help with a value analysis with the finance department to choose the best tool for the budget.
Inter-Cross Functional Team
These teams are formed between a buyer and supplier to create an alliance. They focus on developing shared vision, increasing communication, solving problems, innovation and most off all developing a trusted relationship. These teams help reduce the overall cost to the buyer and supplier, reduce time to market, improve quality, improve technology flow from supplier and improve continuity of supply by increasing overall efficiency. The teams can be a little difficult to form in the beginning but pay dividends when they’re working. These members can include key customers, suppliers, or consultants.
These teams have become a common approach to address many acquisition related activities to include: 
- System development
- Requirements Development
- Funding instability
- Manpower allocation
- Value analysis and Value Engineering
- Standardization and simplification
- Engineering change management
- The development of a Statement of Work (SOW)
- Commodity teams
- The acquisition of capital
- Make or buy outsourcing analysis
- Source selection
- Post award management
- Supplier development
- Development of strategic alliances
- Much more….
- Make sure these teams have a clearly defined charter from senior leadership.
- Make sure the members have the authority to make changes.
AcqLinks and References:
-  Website: Wikipedia – Cross-Functional Teams
-  Burt, Petcavage, and Pinkerton, “Supply Management” McGraw-Hill 2010