Mega Corp: Oh, quite a few.  (Well, bearing in mind the cultural, demographic, and technological differences that mean that while an Earthly multinational might hit millions of employees, its Imperial counterpart probably has a couple of dozen executives, a large computronium core, and millions of jobs being done by subcontractors, sub-sub-contractors, etc., or “on-bounty”.)

The canonical list in the Empire and nearby, the “Big 26” starcorporations, are usually given as:

All Good Things, ICC – retailing

Artifice Armaments, ICC – firearms, heavy weapons, military vehicles, and defense technologies

Atalant Materials, ICC – mining, refining, and nanoslurry production

Biogenesis Technologies, ICC – neogenic organisms, biotech products and bioshells

Biolith Chemical Products, ICC – bactries and organochemicals

Bright Shadow, ICC – computers (including expert systems and thinkers), telecommunications equipment, and infotech

Cognitech, ICC – cognitive science, psychedesign, nootropics, and sophotechnology

Consolidated Mutual Mitigation and Surety, ICC – insurance underwriting and ancillary legal services

Crystal Flame, ICC – immortality (noetic backup archiving and insurance)

Databeat, ICC – major cycle brokerage and information furnace rental org

Ecogenetics, ICC – ecopoesis, living systems, environmental services, and bio-architecture

Enjoyment Unbounded, ICC – entertainment and luxury goods

Experia, ICC – entertainment and media (watchvid, InVid, slinky, and virtuality)

Extropa Energy, ICC – energy production and distribution, antimatter production, and fuels

Gilea and Company, ICC – banking, investments, and futures markets

Llyn Standard Manufacturing, ICC – cornucopias and industrial-scale production

Prosperity Nexus, ICC – investment, fund management, and commercial banking

Ring Dynamics, ICC – stargates (construction, maintenance and leasing)

Riverside Eubiosis Foundation, ICC – pharmaceuticals and health and medical services

Service Gate, ICC – contract matching and labor allocation

Stellar Express, ICC – delivery services, interstellar logistics, supply chains, and shipping

Systemic Integrated Technologies, ICC – robotics, automation, and infrastructure technology

Telememe, ICC – news, statistics, demographics, data mining and information research

Traders in Ideation, ICC – information brokerage, rights management services and data warehousing

Ultimate Argument Risk Control, ICC – security services, military contracting, and mercenary brokerage

Vermilion Harvest, ICC – agriculture, silviculture, carniculture, and bioproducts

…but there are several others that compete close to these leagues – exactly which are named depends on who precisely you’re talking to.

Given the nature of the setting, of course, the traditional unremittingly negative portrayal of business in fiction is utterly averted, and the Big 26 receive the respect they deserve as the mighty prosperity-generating engines that they are.  But then, in their home markets, the free market actually is a free market, so they never had the opportunity to discover corrupt business strategies of monopoly, rent-seeking, and regulating the competition out of business, even if they didn’t tend to be run by people who are every bit as ideological as everyone else in the vicinity.

(Well, not that this opinion is shared by everyone.  Gilea & Co. and UARC, in particular, tend to attract some opprobrium elsewhere in the Associated Worlds, particularly in places that don’t appreciate the absolute sacredness of contract in Imperial ethics, Gilea & Co.’s policy of not recognizing any special difference between “states” and its regular commercial customers, and – especially – its willingness to pursue “asset realization” after a sovereign default with however many of UARC’s finest mercs it takes to impress upon the customer that when they do the job, they always get paid.  But that’s not the mainstream opinion at home.)

As a side note, while it is by no means a conventional corporation, the Imperial Charter makes use of much of the traditional structure of a joint-stock corporation in the Imperial government, such as it is – its citizens, for example, are citizen-shareholders in the technical lingo, and the traditional style of the Imperial Couple includes “Chief Executive Officers of the Imperium Incorporate” – so you could make a convincing argument that the Empire is, in quite a few senses, the biggest Mega Corp of them all.