Suppose I have two base classes B1 and B2, and a class D that derives from both B1 and B2 as follows:
class B1 {
public:
  // ...
  virtual void foo() final { cout << "Hello, B1\n"; }
};
class B2 {
public:
  // ...
  virtual void foo() { cout << "Good riddance, B2!\n"; }
};
class D :public B1, public B2 {
  // ...
};
In designing the class D, I want to override the member function called foo() from B2; however, foo() in B1 is marked final and prevents me from overriding foo() in B2. What is the best approach to override foo() from B2?
I don't think what you want to do is possible in the manner you've shown in the question. From N3337, §10.3/2 [class.virtual]
If a virtual member function
vfis declared in a classBaseand in a classDerived, derived directly or indirectly fromBase, a member functionvfwith the same name, parameter-type-list (8.3.5), cv-qualification, and ref-qualifier (or absence of same) asBase::vfis declared, thenDerived::vfis also virtual (whether or not it is so declared) and it overridesBase::vf. ...
D::foo matches all those criteria for B1::foo and B2::foo, hence it overrides both. And since B1::foo is final, the code is ill-formed. 
One workaround is to introduce an extra level of inheritance. Define a class, say D2, that derives from B2 and overrides B2::foo. Then D can derive from B1 and D2 instead.
class D2 : public B2{
public:
  virtual void foo() override { cout << __PRETTY_FUNCTION__ << '\n'; }
};
class D :public B1, public D2 
{};
D d;
// d.foo();    // error - ambiguous
D2& d2 = d;
d2.foo();   // calls D2::foo
B2& b2 = d;
b2.foo();   // calls D2::foo
B1& b1 = d;
b1.foo();   // calls B1::foo
Live demo
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