For example, the ship's carpenter and his mate are Americans, the Bosun and his mate are from Austria and France, respectively. There are also New Guinean, Russian, Chinese, Danish, Swedish, etc topmen and seamen serving as crewmates.
If I can speak for the Dutch East Indies Trading Company (VOC).
The VOC needed more and more staff to sail to the East. It wasnt just the increase in trade but also the need for Europeans who died relatively fast over there. The VOC needed sailors as well as soldiers.
Between 1630-1640 9% of all available sailors in the Dutch Republic were in service of the VOC. In 1680 this was 18%. With the soldiers (whom the VOC was also always in need of) the share grew from 16% in 1680 to 33% by mid 18th century.
In other words, the Dutch Republic couldnt satisfy the VOC's endless need for more people. On average, over its whole existence its estimated 40% of its sailors and 60% of its soldiers were from outside the Republic. Although there were fluctuations but in 1770 its estimated 80% of its soldiers and 50% were not from the Dutch Republic. In that time over 80.000 people worked for the VOC.
At first the VOC would recruit in other coastal areas like Scandinavia, German Oostzee States, Oostende, Duinkerke. But eventually had to go more inwards. Most foreign workers were either from the Southern Netherlands (present day Belgium and North West France) or German speakers (including present day Switzerland and Kaliningrad).
Challenges were also very much present in Asia itself. Due to the high mortality the VOC also experienced shortages within Asia. For the intra-Asia trade it started to recruit small numbers of Asian staff by the end of the 17th century. This number grew gradually and by 1781 Asian staff was used on routes back to Europe. At first this were usually people from coastal areas from India and Indonesia where the VOC was powerful. This were mostly Asian 'Moors' or Asian Muslims but sometimes also Asian Christians able to speak Portuguese. In the 2nd half of the 18th century more and more Chinese staff was hired. On board there were also usually Asian slaves present (serving the wealthy) and groups of Asian soldiers (the VOC used during its existence a lot of native soldiers for its campaigns. Finding Europeans for this in Asia was obviously even more of a challenge than having enough European sailors.)
There is also a lot written about life on board, tensions between the different nationalities, but you do see quite a number of different nationalities in service of the VOC mostly due to practical reasons.
The VOC ceased to exist in 1799 and was succeeded by the NHM in 1824 focusing again mostly on the Dutch East Indies (present day Indonesia). Unfortunately you are asking specifically for a period at least the VOC didnt exist anymore, as well as the Dutch Republic as a whole (France), but in any case there is no reason to assume this changed fast afterwards. The VOC was particularly unique in its intra-Asian trade and that network needed more and more men and thus foreigners.
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