Lead Conversion and Lead Status Update

Hi, 

I have a question about updating Lead Status during / after lead conversion. 

We convert lead for three reasons:

- they are existing customers (Converted - Customer);

- they belong to an existing opportunity (Converted -  Existing Opportunity);

- they are a new opportunity (Converted - New Opportunity)

Currently, when converting any lead, the Lead Status changes to Converted (without three distinctions which is confusing for reporting).

Is it possible to run a BPM where depending on why a lead is being created the Lead Status will be updated automatically, or is it possible to add the Lead Status field to conversion pop-up window to be filled out by the user? 

Thanks! 

Ada