Multiple Visits for Schengen Business Visa

[Alakazam]

Dear Sir/Madam

If I am issued a Schengen Multiple Entry Business Visa based on a business requirement in Sweden, is it possible to visit other Schengen zone countries if I am called up for an ad-hoc business meetings in those other Schengen countries?

For example:
I am issued the Multiple Entry Business Visa on 25th March 2015.
I visit Sweden for my original business meeting on 2nd April 2015
and then return home to the UK on 4th April 2015.
My boss, who is in Berlin, calls me up the next day (5th April 2015)
and asks me to immediately pack up for a business meeting in Paris scheduled on 7th April 2015.
Since I don't have an invite from the French company, will I be barred from entering France using the same Business visa?

If the French border control does not allow me to enter France under the same visa due to the lack of an invitation from a French company, will a letter from my boss convince the border control agents?

Any guidance on this will be appreciated.

Notes
1. Sweden and France have been used as examples. These 2 can be replaced by any 2 countries in the Schengen zone
2. I live in the UK under a settlement visa.

Thanks
Best regards
Alakazam