Windows live mail at least will do that. It has each account listed seperately on the left and an "All inboxes" or something at the top so you can see everything at once.
My Computer
Computer Manufacturer/Model Number
Scratch built
OS
Windows 7 x64 Ultimate
CPU
i7 960
Motherboard
Asus P6X58D
Memory
12 Gig Corsair Dominator
Graphics Card(s)
Nvidia 480
Sound Card
Maudio Delta 44 + breakout box
Monitor(s) Displays
Dell UltraSharp U2410 24in and Samsung 21 dual monitors
Thunderbird will do that to, you may have to check your individual e-mail service to see if it is allowed I have a Juno account that I can only check through a web browser it will not let me check it through Thunderbird.
Jerry
My Computer
Computer type
Laptop
Computer Manufacturer/Model Number
Sager NP9170
OS
Win 7 Pro x64 / Win 10 Pro
CPU
Intel(R) Core(TM) i7-3630QM CPU @ 2.40GHz
Motherboard
CLEVO P170EM
Memory
12 GB
Graphics Card(s)
(1) Intel(R) HD Graphics 4000 (2) NVIDIA GeForce GTX 675M
Sound Card
(1) Realtek High Definition Audio (2) Intel(R) Display Aud
Monitor(s) Displays
17.3
Screen Resolution
1920x1080
Hard Drives
(1) Samsung 860 EVO 500GB(OS) (1) Samsung 860 EVO 500GB(Data)
Keyboard
Backlite
Antivirus
MSE, Malwarebytes Pro
Browser
Firefox
Other Info
DESKTOP: Custom-built.
OS: Win 10 Pro x64.
CASE: Rosewill R5.
CPU: Intel I5 4670K CPU @ 3.40GHz.
CPU COOLER: Cool Master Hyper 212 EVO.
MOTHERBOARD: Asus Z87-A.
MEMORY: Kingston HyperX 2x4 GB.
GPU: Nvidia Geforce 650 TI.
PSU: Corsair TX750.
DRIVES: (1) Samsung 840 120 GB SSD (2) Western Digital blue 500 GB 7200 RPM.
You may need to change your settings so that it doesn't do that.
As an example on the Gmail account I have you can change the settings so that it saves it or delete it.
That's through the web browser.
Jerry
My Computer
Computer type
Laptop
Computer Manufacturer/Model Number
Sager NP9170
OS
Win 7 Pro x64 / Win 10 Pro
CPU
Intel(R) Core(TM) i7-3630QM CPU @ 2.40GHz
Motherboard
CLEVO P170EM
Memory
12 GB
Graphics Card(s)
(1) Intel(R) HD Graphics 4000 (2) NVIDIA GeForce GTX 675M
Sound Card
(1) Realtek High Definition Audio (2) Intel(R) Display Aud
Monitor(s) Displays
17.3
Screen Resolution
1920x1080
Hard Drives
(1) Samsung 860 EVO 500GB(OS) (1) Samsung 860 EVO 500GB(Data)
Keyboard
Backlite
Antivirus
MSE, Malwarebytes Pro
Browser
Firefox
Other Info
DESKTOP: Custom-built.
OS: Win 10 Pro x64.
CASE: Rosewill R5.
CPU: Intel I5 4670K CPU @ 3.40GHz.
CPU COOLER: Cool Master Hyper 212 EVO.
MOTHERBOARD: Asus Z87-A.
MEMORY: Kingston HyperX 2x4 GB.
GPU: Nvidia Geforce 650 TI.
PSU: Corsair TX750.
DRIVES: (1) Samsung 840 120 GB SSD (2) Western Digital blue 500 GB 7200 RPM.