In the United States (with FAA training), you can hold a PPL Multi-Engine and get a Type Rating on a LearJet (or a Citation). In the USA, if you do not hold an Instrument Rating, you will have to limit your Learjet flying to below 18,000 feet. As far as getting an aircraft insurance that will cover you with the "minimum experience" might be a problem. You may have to hire an experienced "co-pilot" qualified on that Learjet to keep you out of troubles.
xxx
Happy contrails
P.S.
Why dont you do with a 747 rating...? You can do with a PPL as well...