If you still have questions after perusing FAR 91.157, the FAA’s Aeronautical Information Manual may help. Highlights from its discussion (at para. 4-4-6) include:
1. Pilots must request an SVFR clearance; ATC won’t offer it (although controllers may hint at it: ”Is there anything special we can do for you today?”).
2. An SVFR clearance is granted on a traffic-permitting basis. IFR flight operations take precedence and your clearance to enter or leave controlled airspace may be delayed for this reason.
3. SVFR clearances are available in Class B, C and D airspace, plus Class E surface areas only. ATC provides separation between SVFR flights and IFR operations. Regardless, ATC does not provide separation after an aircraft leaves the airspace on an SVFR clearance.
4. Since the pilot must remain clear of clouds, an SVFR clearance will not include a specific altitude. The clearance may include an instruction to fly at or below a certain altitude, due to other traffic, but that altitude will permit flight at or above the minimum safe altitude.