#1
Am Dm E E7 Am

4 bar prog with E and E7 in the 3rd bar


Anyways then I got:

Am Dm E E7 Am A7

But where to go after A7?
#3
I would go with D if you want it to resolve properly.

Although honestly I would throw in a Gm or something, but that's just me.
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#4
you have many options. A7 could be seen as the secondary dominant of D or D Minor. then you could go to G then to C for a quick fifths cycle.

it is also good to look at what is happening in your chord progression. i assume that the progression is in A minor.

Am - the tonic chord or i
Dm - iv
E - V
E7 - V7
Am - i
A7 - I7

so you have general i-iv-V structure and then when you come back to the Am you pull from the parallel major to make I7 (A7). now you can use a quick cycle through A major chords if you want. this is why so many options are open to you. of course your ear is the guide, so don't just assume that the things i say will sound good, try them. here's my idea

Am - i
Dm - iv
E - V
E7 - V7
Am - i
A7 - I7
A#7 - taken from tritone substitution of E7
B7 - secondary dominant of E7
E7 - V7
Am - i

just a thought. (hopefully i got the tritone sub correct!).
#6
Quote by bangoodcharlote
Just so you know, you're changing the key by playing A7 wather than Am or Am7.

But you could go A7, Dm, G, Am.


are you shifting into C major there?