Is it possible to overlap shader effects in OpenGL ES 2.0? (not using FBOs)

How to use the result of a shader with another shader without having to do a glReadPixels and push again the processed pixels?

The next pseudo-code is what I'm trying to achieve:

Code :
// Push RGBA pixels into the GPU
glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, width, height, 0, GL_RGBA, GL_UNSIGNED_BYTE, Pixels_To_Render);
 
// Apply first shader effect
glUseProgeam( FIRST_SHADER_HANDLE);
glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 
// Apply the second shader effect by sampling from the result of the first shader effect
glUseProgeam( SECOND_SHADER_HANDLE );
glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
 
// Get the overall result
glReadPixels(......)