Question: Is is possible to have multiple non-Immigrant category B visas for employment for Thailand at the same time? 

I got an employment offer from a company in Thailand, and applied for a non-Immigrant category B visa with their invitation letter at the local VFS center in India. However a week later, I got another better offer from another company in Thailand itself? 

Can I use the existing visa to go work for the other company? Or apply for another visa of the same category while there is an existing valid one in the same passport?

Answer: 
Usually non-immigrant Category B visas for employment have the name and position of the company you are going to work for written on them. While this does not mean you cannot use the visa to enter Thailand, you will have trouble applying for a work permit for the second company after coming to Thailand.

Also, you cannot have an existing valid visa of the same type while applying for visa on behalf of the second company. In this case you will have to explicitly get the first visa voided (cancelled) before applying for the second one. All this can be carried out at the VFS center itself.
A visa is not attached to a particular company. Once it is issued, you can use it to enter.

Note that this is different from an extension of stay which is done at a local Thai immigration office. Extensions are tied to the reason of extension. So if you are extended by reason of employment, the extension is voided as soon as your employment ends (fired/quit). Similarly, if you extended by reason of marriage, that extension is invalid the day the divorce is finalized. 

You dont automatically get 7 days to leave the country. You must apply for that 7 day extension at the local immigration the next business day. 

This is why some people opt for a Multiple Entry [ME] Non Immigrant visa (Non-B in your case) vs a 1 year extension of stay. If you get fired or quit, your visa is still valid. Just tell your employer that every 89-90 days you will need time for a border hop. 

Not sure how easy ME Non-imm will be to get for Indian national though. Even if they do issue ME non-B, sometimes the neighboring Thai Embassies will want to see 8-10 months remaining on the work permit as a condition to issue ME.