Really it's hard to say whether a corporation would do this or not, but take a look at this list and you can see there surely could be. As with JP Morgan vault, banks do this all the time. I don't believe we are told in Die Hard what actually happens at Nakatomi Plaza, but they could be some sort of banking firm. What seems the most unlikely about the scenario of the movie is placement of the vault itself. A more likely place for it would be underground in a basement level, for two major reasons. First of all, security. If you have concrete and ground on four or five sides of the six sided vault, it would make it a lot more secure than having high up in a structure. The second would be what it would take to support a structure inside the upper reaches of a building. In order to create a vault as they described in Nakatomi Plaza, it would have to be pretty massive. Theo cuts through a bunch of layers, then waits for the "miracle" of the F-B-I which Hans gives him in order to get through the magnetic seal to actually get into the vault (IIRC). This makes for one heavy chunk of vault, which would have to be suspended somewhere in the building, which is very unrealistic in architectural terms.
It would make sense for a corporation to diversify their holdings if they have the money. If they did diversify, they would probably want to have some of that local and easy to get to. Bearer bonds are real, though the US no longer issues them. A corporation could very well hold bearer bonds, but even in the late 80's probably not very realistic. Electronic transfer of funds was probably more used those days, and it would be absolutely the mode of transfer today. In the Wiki article, it says the main reason for bearer bonds was the untraceable transfer of money. A corporation like Nakatomi probably wouldn't have been using them in the first place.
One of the problems you are going to see is if a corporation does store valuables in their own vaults, we (the public) probably wouldn't know too much about them. These corporations want to keep their valuables, well, theirs. The only way the public would probably find out about such vaults is if someone on the inside divulged the information on the vault, but I would bet these people have to sign non-disclosure agreements to keep this information from the public light.
So, bottom line, is it possible? Yes. Is it plausible, maybe not. Will we ever know for sure ... as yet untold, but probably not.