I don't understand your situation and you have provided little detail from your first experiment, but here are my thoughts/questions. First why do you care to "extend" the first experiment? It seems like factor A is the only factor you want to include in the next experiment. The inference space may be completely different.
1. For your factor "A" you found that the lower value was best. How many levels was this factor tested at? It seems like you want to experiment with an even lower value of A? Were there no interactions?
2. You discovered B, C and D were not useful (e.g., significant), so you want to drop them from consideration. How "bold" were the other factor levels in your experiment? Where will you set them?
3. You want to add 2 new factors E & F and then also add the factor that was constant win the first experiment. While this can be done, you will miss any possible interaction with the B, C and D factors. Also the significance of A is conditional. Its significance depends on the other terms in the model and how you estimated the MSE. If either of those change so may the importance of A.
4. In retrospect, you should have experimented on the constant , E and F in addition to A, B, C, D in the first experiment. Then decisions to remove terms are more effective.
"All models are wrong, some are useful" G.E.P. Box