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A tad awkwardly :

sage: sum([v[0]*SR("u")^v[1] for v in (c0 * (x+1) + c1*(x+1) + c2*c1*x - c0*c1*
        (x+1)).subs(x+1==SR("u")).coefficients(SR("u"))]).subs(SR("u")==x+1)
c1*c2*x - (c0*c1 - c0 - c1)*(x + 1)

This can be programmed as :

def mycollect(e1, e2):
    """
    Collects e2 coefficients in e1, even when e2 is not a factor of
    some of the terms of e1
    """
    g = maxima_calculus.gensym()._sage_()
    while g in e1.variables(): g = maxima_calculus.gensym()._sage_()
    return sum([v[0]*g^v[1]
                for v in e1.subs(e2==g).coefficients(g)]).subs(g==e2)

Test :

sage: mycollect(c0 * (x+1) + c1*(x+1) + c2*c1*x - c0*c1*(x+1),x+1)
c1*c2*x - (c0*c1 - c0 - c1)*(x + 1)

This (with some possible generalizations) might become a new method for symbolic expressions. Advice ?

HTH,