The British East India Company did exactly this. The Company was privately owned and none of the shares belonged to the British government. They first set up operations in India in the 17th century and traded in various products. By the middle of the 18th century, they found themselves in a dispute with the ruler of Bengal and fought the Battle of Plassey in 1757 against him. The Company won, and took over the province. They cemented their rule with the Battle of Buxar in 1765.
The East India Company did not limit themselves to India either. They traded with China for many goods, chiefly tea and porcelain. By 1800 the Company was buying 23 million pounds of tea per year at a cost of 3.6 million pounds of silver. Concerned that the China trade was draining silver out of England, the British searched for a counterpart commodity to trade for tea and porcelain. They found it in opium, which they planted in large quantities in Bengal. Over the next few decades, opium smuggling into China became a huge money spinner for them. In 1773, they were exporting 140k lbs of opium from Calcutta in India to Canton (Guangzhou) in China. This gradually rose to about 5.6m lbs in 1839. That was when the Chinese emperor decided to outlaw opium smuggling, and sent Commissioner Lin Zenxu to deal with the situation. Lin got to Canton, seized and destroyed vast quantities of opium and closed the port to the British. This led to the First Opium War, which which lasted 3 years. It was a bloody affair, and the vast majority of casualties were on the Chinese side. Most of the fighting was done by men employed by and ships owned by the Company.
The Company did quite well for itself while it lasted, especially with the opium trade. However, it bore the brunt of the blame for the Rebellion in India that took place in 1857. The direct result of that was the Government of India Act (1858) that effectively nationalised the company and made Queen Victoria Empress of India. When the company finally dissolved in 1874 The Times reported It accomplished a work such as in the whole history of the human race no other company ever attempted and as such is ever likely to attempt in the years to come.
Sources - The First Opium War by Peter C. Perdue
I wrote an essay about globalization in the 17th century for my undergrad, here is a small part of it which will help answer your question
"Inter-state competition was one of the hallmarks of the 17th century, such competition was definitely at a result of the growth of trading companies which allowed for imperialism without the expense. Such companies allowed nations to increase their power overseas but without having to bare many of the costs and administrative difficulties involved, in many ways the process could be called ‘privatised imperialism.’ The Netherlands being the most successful nation of the 17th century gives the best example of this kind of expansion. The Dutch West India Company (WIC) is a good example of the privatised imperialism concept, unlike the VOC the WIC’s military role against the Iberian Atlantic was established at its inception in 1621. The idea that trading companies were used to enact foreign policy is very interesting it shows how Early Modern States adapted to the new challenges presented by globalization. The VOC and WIC targeted the possessions and trade of the Iberian states, most of the efforts being directed towards Portugal the ‘original’ maritime state. So successful were WIC efforts that the Netherlands’ was able to occupy and begin colonization of parts of Brazil previously owned by the Iberian union, this territorial change was supported by the Treaty of Münster (1648). Boxer writes that the Treaty “forms the high-water mark of the United Provinces’ golden age.” This may seem irrelevant to the question of globalization, but through the use of two multinational corporations the Netherlands now controlled territory from Nagasaki to New Amsterdam (New York), an impressive achievement making the globe seem all that much smaller. The Dutch had also managed to supplant the Portuguese monopoly on spices and “practically maintained a monopoly on the spice trade in the East throughout the seventeenth century.” The Dutch experience certainly supports the assertion that globalization began in the 17th century especially when considering their flourishing overseas trade and empire. In spite of Dutch superiority throughout the 17th century the English also saw some success in displacing rival powers. The Battle of Swally (1612) was an important milestone for England and its eventual dominance of India, and also for the transformation of the trading company from simple merchants to what could anachronistically be called ‘private military contractors’ or “private navies”. The battle although seemingly small in scale caused the Mughal court to grant the EIC trade rights and a small amount of land at the expense of the Portuguese Empire. These gains were further reinforced after unsuccessful Portuguese counter attacks in 1614. The military wings of trading companies provide much evidence for how Early Modern States exerted their power on the world, the global reach of trading companies meant that conflicts originally confined to Europe, such as the old Mediterranean trade rivalries were now replaced by struggles on a global scale."
Sources:
Boxer, C. R. The Dutch Seaborne Empire 1600-1800 (London, Hutchinson & Co. 1965)
Mukherjee, R. The Rise and Fall of the East India Company (Berlin: VEB Deutscher Verlag Der Wissenschaften, 1955)
Black, J. Naval Power (London, Palgrave-Macmillan 2009)
TLDR: Trading Companies in the 17th century were an extension of the state from which they were formed. When that state went to war, they went to war. They also formed a key part of that states foreign policy and would later be the backbone of Empire.