We propose a solvable aggregate growth model with the rate keel K(i;j; l) ∝ iμjνl(B) ((B) ≥ 0), at which a monomer transfers from the A aggregate of size i to the A aggregate of size j only with the help of a B aggregate of size l. By means of the mean-field rate equation approach, we obtain the analytical solutions of the aggregate size distributions in several different cases. For a symmetrical system with μ = ν, the aggregate size distribution aκ(t)approaches the conventional scaling form in theμ＜ 3/2 case; while for an asymmetrical system withμ≠ν, aκ(t) takes the scaling form only in the case of μ＜ν andμ+ν＜ 2. As for the case withμ+ν＞ 2 (μ≠ν) orμ＞ 3/2 (μ = ν), the system may have a gelationlike transition. Moreover, we also study the kinetic scaling behaviour of the model with the generalized keel K(i; j; l) ～ (iμjν + iνjμ)l(B). The aggregate size distribution obeys a scaling law only in theμ + ν＜ 3case; while in other cases, the system may undergo a gelationlike transition after a sufficiently long time.