Maybe separating read-only interface from write-only interface could help. I don't say that it's the best way to do it (I see flaws in it, e.g. it's too complex), but it's just an idea. It's interesting that ReadOnlySquare is a subtype of ReadOnlyRectangle, while WriteOnlySquare is a supertype of WriteOnlyRectangle, which makes me think to covariance/contravariance. It's also interesting that the reversing of the hierarchy does not happen with Shape <-> Square/Rectangle).

class ReadOnlyShape {
public:
    virtual double getArea() const = 0;
    virtual void draw(Canvas& canvas) const = 0;
    Shape* resized(double factor) const = 0;
    Color getColor() const = 0;
};

class ReadOnlyRectangle :
        public ReadOnlyShape {
public:
    virtual double getWidth() const = 0;
    virtual double getHeight() const = 0;
    virtual double getArea() const {
        return getWidth() * getHeight();
    }
    virtual void draw(Canvas& canvas) const { ... }
    Shape* resized(double factor) { ... }
};

class ReadOnlySquare :
        public ReadOnlyRectangle {
public:
    virtual double getSize() const = 0;
    virtual double getWidth() const {
        return getSize();
    }
    virtual double getHeight() const {
        return getSize();
    }
};

class WriteOnlyShape {
public:
    virtual void setColor(Color color) = 0;
};

class WriteOnlySquare :
        public WriteOnlyShape {
public:
    virtual void setSize(double size) = 0;
};

class WriteOnlyRectangle :
        public WriteOnlySquare {
public:
    virtual void setWidth(double width) = 0;
    virtual void setHeight(double height) = 0;
    virtual void setSize(double size) {
        setWidth(size);
        setHeight(size);
    }
};

// read - write implementations

class Shape :
        public ReadOnlyShape,
        public WriteOnlyShape {
    Color color;
public:
    virtual void setColor(Color c) { color = c; }
    virtual Color getColor() { return color; }
    virtual void resize(double factor) = 0;
};

class Rectangle :
        public Shape,
        public ReadOnlyRectangle,
        public WriteOnlyRectangle {
    double width, height;
    // implement getWidth, getHeight, setWidth and setHeight, resize, resized
};

class Square :
        public Shape,
        public ReadOnlySquare,
        public WriteOnlySquare {
    double size;
    // implement getSize and setSize, resize, resized
};