Yes! You can charter large aircraft like the 747. A lot of airlines offer this service for large groups (sports teams come to mind), and there are also operators of the Boeing Business Jet that were created just for private and charter uses.
The TSA requires aircraft like this to adopt a security program called the Twelve-Five Standard Security Program (or TFSSP for short).
49 CFR Part 1544 contains the regulations which cover this.
Most of the security program falls under non-disclosure rules that prevent anyone with knowledge of the program from talking about it to people that don't have an operational need to know (and have also signed a non-disclosure). This helps to prevent people that would try to bypass the security measures in place from even knowing what to look for.
The regulations do specify the following though:
- Each operator of an aircraft that weighs more than 12,500 lbs. that is used for scheduled or charter operations must adopt the program.
- The program must be approved by the TSA.
- The program must contain the procedures and description of the facilities and equipment used regarding:
- the acceptance and screening of individuals and their accessible property, including, if applicable, the carriage weapons as part of State-required emergency equipment,
- the acceptance and screening of checked baggage,
- the acceptance and screening of cargo,
- the screening of individuals and property,
- the use of metal detection devices,
- regarding the use of x-ray systems,
- the use of explosives detection systems,
- the responsibilities of security coordinators,
- the requirements for law enforcement personnel,
- carriage of accessible weapons,
- carriage of prisoners under the control of armed law enforcement officers,
- transportation of Federal Air Marshals,
- aircraft and facilities control function,
- the specific locations where the air carrier has entered into an exclusive area agreement,
- fingerprint-based criminal history records checks,
- personnel identification systems,
- an aviation security contingency plan,
- bomb and air piracy threats,
- flight deck privileges, and
- the Aircraft Operator Implementation Plan (AOIP).
As you can see, there is quite a bit that goes into the TFSSP. Two of the biggest things though are the requirement for all flight crew members to undergo a fingerprint based criminal background check and that access to the flight deck must be restricted.
For more details, refer to the actual regulations which cover this in more depth.
NBAA also has a page about the TFSSP.