Yes, there is no reason why it would not be possible.
However on the form, there is a specific field to list the visas delivered during the last 3 years (field 26?). Just list your multiple entry visa there: validity date from... to...
The application form is here:Schengen Visa Application Form.
They explicitely expect that people would have already got an issued visa previously (see field #26), they do not mention the validity dates of this previous visa, thus the question falls in this case.
Now it is not possible to give a "proof" that it will work, because the countries reserve for themselves the right to refuse a visa without any reason nor explanation, to whom they want whenever they want... The only way to deal with the problem is just to fill correctly the form, including the mention of a previously issued visa for a later period.