There is no way to sponsor yourself on an H-1B. It must and can only be through a U.S. Employer.

Please read our blog post- Ensuring Your H-1B Cap Subject Petition is Properly Filed

The regulations allow an individual in H-1B to work two or more jobs by filing an H-1B petition for "concurrent employment". We could assist you with this process if the job rises to the level of a specialty occupation and your employer is willing to file a concurrent H-1B petition on your behalf.

Q: My wife just joined a new company and received new I94 which has expiration date of March 2015. However she is approaching her maxout time period of 6 years and maxout date falls in Oct 2014. Based on new I 94, does this mean her maxout date is March 2015 and not Oct 2014? [...]

The key is to document the existence of an "Employer-Employee Relationship" and the ability of your employer to control your employment at the client site. This may be documented through a letter(s) from the End Client, or a chain of contracts from the employer to the end client.

I came in United States in February 2013 with Employer A (H1 B valid till Sept 2015) and joined Employer B in November 2013(Got new H1 B visa valid till September 2016). In December 2013 went to India for vacation and did not get my visa stamped with new employer(B)... because my old stamp was [...]

The I-94 is known as the arrival-departure record and will be taken from you at the POE (Airport).

A photocopy should be sufficient.

Two distinct employers would be treated as having filed two distinct petitions. The two should be completely unrelated and not rely on the same end client documentation/contract(s).

Unless there is a specific instance of fraud, the USCIS does not randomly call employers to verify the contents of an experience letter.