If you have a country with unique needs for some kind of weapon system but it doesn't have a domestic industry to produce it, is it possible to fund the development in a friendly foreign country?
Germany managed to fund, research and develop their early tanks in Russian tank schools and factories (of all places) after being not allowed to work on them in Germany following the Treaty of Versailles.
So I think it's proven that you can "fund custom weapon development in a friendly foreign country". I'd even say "friendly" is optional.
The point of the domestic military industrial complex is to create jobs and maintain your own nation's technological lead. If your nation doesn't have the technology, you try to acquire it. If your nation doesn't have the industrial base, you build it.
Maintaining the military industrial system may appear to be money down the drain, but it's money down the drain within your domestic economy, it stays within the domestic economy for some time and, directly and indirectly, employs a lot of people. It's tax money that goes straight back to the population. You buy the raw materials from your own mines, even if someone else is cheaper. You contract your own factories, your own shipyards. Keep the money in the country and keep it moving around entirely within the domestic economy as much as possible.
One may buy in complete weapons systems, often aircraft, but one very rarely funds someone else to develop it, as that's paying for someone else to have a technological lead over you.
You mean like France building a ship for Russia? Or Israel for... well anyone who want to buy UZI? Or Poland organizing an auction for possible choppers?
Yes Everything is possible if you have money.
You can order totally custom piece of equipment (with brand new R&D), you can order custom build of existing one or you can just get one off the shelf.
But remember to not attack manufacturer country with the weapon they made for you. They are the first one to have a counter measure for that.