Getting a UK visa when the company is HQ in continental Europe

I'm an American in London on a Tier 2 visa, and have a Finnish company that would like to hire me that is not Tier 2 eligible now. Are there any options for us?

The company would need to apply for a sponsorship license.

What are the requirements for an EU entity, though? The UKBA site only discusses UK businesses. Are there are any companies that specialize in helping with this?

What are the requirements for an EU entity, though? The UKBA site only discusses UK businesses.

It's the same as a UK business. As KFdancer said "The company would need to apply for a sponsorship license".

What Tier 2 visa are you on? General or ICT? If it's ICT, when did your visa start?

As Sirius is pointing out, first you need to find out if you are eligible to change sponsors in country and without the 12 month cooling off period outside of the UK.

If you are able to change sponsors, the company would need to obtain a sponsorship license.  Yes, there are lawyers who can help with this.  The company has to meet a list of criteria.  There would be considerable time and expense on their part.  Are they willing to wait and spend the money?

An agency quoted these rates today for the process, but I'm wondering if this is competitive?

Capital Visas Fees:
 
- License = £1200 + VAT
- COS = £300 + VAT
- LMT = Not required
- Workpermit = £995 + VAT (Premium - Same-day)
 
Government Fees:
 
- License = £536
- COS = £184 per applicant
- LMT = N/A
- Workpermit = £514 + £400 per applicant
 
Processing Times:
 
- License = Approximately 3-4 Months
- COS = Immediately
- Workpermit = Same-Day.

The rates seem reasonable but the time frames are aggressive.  A new license can easily take 6 months.  Yes, you can do a same day appointment (for a Tier 2, not a work permit) but it will likely take a couple of weeks to get an appointment.

Have you ensured you are eligible to change sponsors in the UK?  The UKVI have clamped down the requirements over the years.