Append separate T-test results using esttab

Question

Please, I would like to append the results from several t-tests in one table using esttab which is from the Stata Journal. I have done the following:

sysuse auto

first, test that price=turn

quietly{
ttest price=turn
preserve
expand 2, g(new)
gen diff= cond(new, turn, price)
eststo m1: mean diff if !new
eststo m2: mean diff if new
eststo m3: estpost ttest diff, by(new)
esttab m1 m2 m3, se mlab(actual predicted ATE) coeflab(diff "private")
}

second, test that trunk=turn

Code:
quietly{
ttest trunk=turn
preserve
expand 2, g(new1)
gen diff1= cond(new1, turn, trunk)
eststo m4: mean diff1 if !new1
eststo m5: mean diff1 if new1
eststo m6: estpost ttest diff1, by(new1)
esttab m4 m5 m6, se mlab(actual predicted ATE) coeflab(diff1 "public")
}

To put the two tests in one table, I have done this:

esttab m1 m2 m3 m4 m5 m6, se mlab(actual predicted ATE) coeflab(diff "private" diff1 "public")

which yields:

---------------------------------------------------------------------------------------------------------
> ---
                      (1)             (2)             (3)             (4)             (5)             (6)
>    
                   actual       predicted             ATE              m4              m5              m6
>    
---------------------------------------------------------------------------------------------------------
> ---
private            6165.3***        39.65***       6125.6***                                            
>    
                  (342.9)         (0.511)         (342.9)                                                
>
public                                                              13.76***        39.65***       -25.89
> ***
                                                                  (0.497)         (0.511)         (0.713)
>

> ---
N                      74              74             148              74              74             148
>

> ---
Standard errors in parentheses

p<0.05, ** p<0.01, *** p<0.001

But this is not quite what I want. I want the result of the second test placed directly under the same three columns as the first i.e the actual, predicted and ATE columns (in other words m4, m5 and m6 respectively are the 'actual', 'predicted' and 'ATE' from the second test). For simplicity this example invloves just two separate tests. But my work involves several of such tests.