For example you don't have to use the amount field anymore, just use the witness part. A witness version X (like 3) could do it by assigning the first witness item to be the fraction amount. In case of two 1.9 and 1.9 inputs the fractions go in the witness item and become 0.9+0.9=1.8 and the old part (the amount in each txout) is still 1+1=2. Both nodes are happy.