When a company (especially a multi-national) takes more than three weeks to get in touch with you, there is a very good chance they've lost interest. It's annoying, but they very rarely get in touch to tell you they've lost interest. All I can say is that you become desensitised to this over the length of your career, but it's horrible the first time.
That said, there is a possibility that you've got lost in the bureaucracy there, so maybe it's worth giving them a call. I can't think of anything you have to lose.
You have a secure offer, you can't keep them holding on forever, so put a bit of pressure on the multi-national. Give them a call, be honest about the situation, tell them that you really want to choose them but, if they don't make an offer soon, you have to take another job before you lose the opportunity.
If they don't get back to you within a day or two then there are only really three possibilities.
- They really have lost interest.
- They are arrogant enough to think they can pull you away from any job when it suits them.
- Their bureaucracy is dangerously destructive to their business and without regard for people.
Regardless, by that point, you should probably take the other job and ignorereject any further contactoffer from the multi-national.