The motor cortex can quickly adapt to perform variations of learned movements, for example by changing the speed or temporal order of muscle activations. The timescale of such adaptation is faster than can be explained by synaptic plasticity, making neuromodulation a prime suspect. Neuromodulation is typically modeled as gain changes at the level of somatic activation function. As a result, gain control is limited to the number of neurons N and often proves to be too coarse for multi-muscle coordination. Moreover, somatic gain modulation cannot easily accommodate the simultaneous impact of different types of neurotransmitters on a single neuron. Here, we explore a more flexible model of synaptic modulation. With N^2 available degrees of freedom, this model provides a unifying framework with tractable multi-modulation control in recurrent rate networks with biological constraints. We introduce synaptic modulation as an element-wise product between the modulation matrix M and circuit connectivity W. The M is obtained from a linear combination of fixed matrices that indicate synaptic susceptibilities to a particular neuromodulator. The activity of modulatory neurons serves as the coefficients in the linear combination, indirectly adjusting connectivity through susceptibility matrices. In a linear regime, somatic modulation corresponds to synaptic modulation where each susceptibility matrix has only a single non-zero column, limiting potential targets of modulation, even with excessive modulatory control. However, with the same amount of parameters, and fewer modulatory neurons, synaptic modulation patterns can efficiently control circuit connectivity, allowing to accurately reproduce different degrees of the movement variation. Our results demonstrate that combinations of static neuromodulatory patterns may optimize rapid adaptation in recurrent neural circuits, incorporating in a single framework --and outperforming-- previous models of neuromodulation.