Reboiling will increase bitterness of all the hops that went in 'late' in the kettle. Obviously, as you said you'll lose your aroma charge will decrease in proportion to the length of the reboil.
You may likely increase the maillard profile of the malt character depending on how long you boil. The complexity of the original grist will dictate the extent of that impact on flavor.
And depending on how much of the 10L you plan to boil off, your mineral content will certainly change as well. Again, depends of the mineral profile of your base water as to the total effect on the beer.
Depending on how long you plan to reboil you may expect to re-dissolve some protein into the beer. (Some of the early Lambic and Belgian brewers would conduct really long boils that drove some portion of the protein in the hot break to break down further allowing it to no longer be break but be soluble peptides in the beer, changing the mouthfeel). This again is base beer dependent along with length of boil.