If the force of friction is 20 N for a moving body does acceleration increase with the increase of the mass? A body is moving and the only force acting on it is the force of friction.
If we put another body on this moving body somehow the force of friction will increase;
does its acceleration change?
 A: The force of friction will increase with the addition of the second mass. However, the mass of the system will increase as well, and the net effect is that the acceleration does not change. To see this, note that:
$$a={F \over m}={\mu _kmg \over m}=\mu _kg$$
Where $\mu _k$ is the coefficient of kinetic friction between the moving body and the surface it's sliding on. Notice that it is completely independent of the mass and the frictional force. Thus, changing the mass has no effect on the acceleration.
A: How the acceleration change may depends on the relation between the two bodies' mass and the coefficient of  friction of the surfaces. I will assume the initial friction is exerted by ground. In the following I use U means upper body (your second body), L means lower (your first body), G means ground, 2 stands for 'to'(or any other prepositions).
1.If U is put with initial velocity lower than that of L which means the there's friction between 1st and the 2nd body. 
So in this case, L will decelerate because of the friction from both ground and the U.$a_{L}=\frac{F_{U2L}+F_{L2G}}{m_L}$. After the upper one get its velocity the same with the lower one, the friction between the two bodies disappears but there's still friction from the ground.Then to the whole system incl. the two bodies, the $a_{final}=\frac{F}{m_{total}}=\frac{\mu m_{total} g}{m_{total}}=a_{original}$
2.If U is put with initial velocity higher than L's,there's still friction between the U and L. But there's difference.The changed accerleration can be calculated in the following expression.$a_{L}=\frac{F_{L2G}-F_{U2L}}{m_L}$. Note this expression, if the value is positive, it means L  decelerate, if it's positive, it accelerates. And also after velocities of U and L get the same, the acceleration of the whole system gets the same as original.
3.If U has exactly same velocity as L, that's easy, the acceleration will keep.
