My employer is a foreign company without a presence in the US. Can they sponsor an H-1B?

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Yes. Anybody can be an employer in the US. Of course, the foreign company will still have to comply with all US laws, pay the US prevailing wage, withhold taxes, get an employer ID number etc. This, for all practical purposes, makes the foreign company a US employer just like anybody else.

Can I open my own company and have this company sponsor me for an H-1B?

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Technically, yes. USCIS will usually scrutinize such situations carefully, though, and a good attorney is critical to get such a case passed. Also, be aware that all the regular restrictions on H-1Bs still apply:

• You can only perform the work specified in your H-1B petition. In particular, you will usually have to hire a manager, accountant, etc. to actually run the business side, unless you have a relevant degree.
• You need to pay yourself a salary at the specified rate no matter how well or poorly the business is doing.

Another point to keep in mind: such an employer cannot sponsor a Green Card.

I am not married to my domestic partner. Can I still bring him or her?

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Possibly. Do be aware that your partner will not be able to later get a Green Card based on yours. As a non-immigrant, however, it is sometimes possible to bring a domestic partner. The domestic partner would apply for a tourist visa at a US consulate, and continue extending tourist status until the primary partner's status ends.

Please note that this is very much a discretionary decision. Therefore, it is not guaranteed that you will actually get a tourist visa for this purpose.

Also note that this process requires an actual tourist visa, even if you are from a visa waiver country. While usually consulates in visa waiver countries are reluctant to issue tourist visas because somebody who claims to be a tourist for a very long time could be considered "suspicious" of immigration intent, joining a non-immigrant domestic partner is a valid reason and should get you past this threshold. Similarly, extending the tourist status even multiple times tends to be more likely to be approved because of the tie to a non-immigrant.

Can I bring my family?

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Most long-term non-immigrant categories have provisions for dependents. This includes spouses and minor children (under 18 or 21 years of age).

What kind of visa is there?

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There are a number of visas that allow working in the USA. The most important ones are H-1B, L-1. You can sometimes also work with a J-1, J-2, L-2, F-1, M-1, I, A or G type visa. For more information on visa types, see my visa types page.