y1 = a1 + b1*x1 + c1*x2 + d1*x3 + u1

y2 = a2 + b2*x1 + c2*x2 + d2*x3 + u2

y3 = a3 + b3*x1 + c3*x2 + d3*x3 + u3

If x1, x2, and x3 are in all three equations (as above) best estimates are just OLS

If not all x's in all equations but u1, u2, u3 are uncorrelated, best estimates are
   just OLS.  

Otherwise, can do better by using information in the covariance matrix of 
   the u's---generalized least squares (GLS).  

If, say, b1 = b2 = b3, this constraint can be imposed when the system is estimated
by GLS.    

If the u's are jointly normal, maximum likelihood can be used.