While on B1 in the US and been offered an opportunity is it possible to apply for an L1 while still in the country? or any type of VISA which gives an opportunity for work?
That is an extremely broad question. The answer is, who knows. Try reposting and be more specific.
The answer provided is general in nature and should not be construed as legal advice as not all facts are know by the attorney, nor does the answering of this question create an attorney client relationship.
In these cases, it is generally better to return to your home country and apply from abroad, since your intention when landing was to come in for a short time for non-work purposes. If you had a change of circumstances, and if there are very good reasons for staying in the U.S., and applying for a change of status after 60 days, then they should be discussed with your immigration attorney. This is indeed a very broad question and depends on various factors, so my advice would be to consult with an immigration attorney and discuss your options.