This paper focuses on the problem of separately modulating and jointly estimating two independent continuous-valued parameters sent over a Gaussian multiple-access channel (MAC) under the mean square error (MSE) criterion. To this end, we first improve an existing lower bound on the MSE that is obtained using the parameter modulation-estimation techniques for the single-user additive white Gaussian noise (AWGN) channel. As for the main contribution of this work, this improved modulation-estimation analysis is generalized to the model of the two-user Gaussian MAC, which will likely become an important mathematical framework for the analysis of remote sensing problems in wireless networks. We present outer bounds to the achievable region in the plane of the MSEs of the two user parameters, which provides a trade-off between the MSEs, in addition to the upper bounds on the achievable region of the MSE exponents, namely, the exponential decay rates of these MSEs in the asymptotic regime of long blocks