The PHB (pg. 151) states that a Cleric may use a shield with a holy symbol as a spellcasting focus:
A cleric or paladin can use a holy symbol as a spellcasting focus, as described in chapter 10. To use the symbol in this way, the caster must hold it in hand, wear it visibly, or bear it on a shield.
And a Warlock may use an arcane focus in the form of a staff. This staff can be treated as a quarterstaff based on what I've gathered, and even applying the description of an improvised weapon, one could deduce that this could double as a quarterstaff for melee attacks.
In many cases, an improvised weapon is similar to an actual weapon and can be treated as such. For example, a table leg is akin to a club. At the DM’s option, a character proficient with a weapon can use a similar object as if it w ere that weapon and use his or her proficiency bonus.
In combination with this prior question and it's answer: Can the arcane/druidic focus staff double as quarterstaff?
Now, could said multiclasser wield a holy symbol shield in one hand, and an arcane focus staff in the other and still be allowed to attack with said staff, and cast spells with both foci without taking up the Warcaster feat? I haven't found any RAW stating that this would NOT be possible, but I'm curious to see if anyone else has.