You have tons of options coming from android if you want better sound, starting from entry level enhancements like a Dragonfly dongle DAC (which I wouldn't use with pretty much any Hifiman headphones) all the way up to a Chord Mojo portable amp/dac and even beyond. If you want to drive more serious headphones properly though, you're going to have to do something, because unless you want to wade into the sea of IEM options out there, most proper full size headphones that are worth listening to need more juice than your android phone can provide. Also, if I had to choose between the HE400SE and the SHR840A I'd take the Shure in a heartbeat. The 400SE have an issue where if the mix is very complex the sound kinds of bunches up, sounds muddy, and you lose the sound stage. The 400SE lacks bass punch which is fine for most music but if you put something like "Who am I" By Beenie man on, you're going to be a sad panda. The 400SE delivers a very relaxed non-speedy sound that is usually detailed and does great work with vocals end electric guitar especially but they run into issues with a lot of music. An example of a ridiculously cluttered track is Champagne supernova by Oasis. On the 840A it still sounds organized but feed it to the 400SE and it just becomes a swamp in the most complex parts.Basically what I'm saying is, the 400SE is not a "This is my only headphone" headphone. It doesn't meet the cut for that. It does a lot of things really well, but it does too many things badly to be your "only headphone" and it's also seriously non ideal to run off mobile without investing $$ into a proper mobile amp. The 840A also gives you several advantages over the 400SE and Grados- it's closed back, so you can take it on the bus and not bother people. It's easier to drive than the 400SE. Buy a dragonfly, and you're going to be good. Also, based on my experience with the SR80 and 400SE and even 400i I can confidently say that the Shure's sound "right" with more music, more often, than either of those other headphones, while also offering better bass. I don't have experience at home with that many headphones long term, but I have listened to pretty much all the major full size headphones at the headphone shops in my city at some point. I don't like talking about most of them though because I have maybe 4-5 tracks each on them and not 3500 like on the stuff I use at home.

Another thing that I think is worth mentioning is that, depending on what you're looking for and how far you want to stretch your budget, bluetooth headphones have gotten gooooood in the last couple of years. Really really good. All the ones that are worth buying are $300 USD and up, BUT, you have a few advantages on hand. 1) You buy ONE thing and you're done. They sound right out of the box because they are self amplified. No need to buy any dongles or anything which means more junk to stuff in your bag or pocket. 2) No cables! No more getting tangled in cables or snagging the cable with your leg and ending up with headphones on the floor. 3) They always sound right. No fiddling with "Should I get THIS dongle DAC or that dongle DAC. But so and so said it sounds better with XYZ. It's a pain free experience.

My personal favourite full size bluetooth headphone that I own is the Sennheiser Momentum 4- but it's firmly in basshead territory. It has classic veiled Sennheiser upper treble and very prominent and tight sub-bass- but not in a way that makes the mids sound crappy. These headphones are phenomenal for electronic music IMO and they do vocals in a very pleasing way. Battery life is up to 60 hours and they charge fast on USB C. Call quality on these is the best regular phone call quality I have ever heard absolutely anywhere. Idk how they do it but they make crappy phone audio sound like a skype call. It's magic. Also if you're walking downtown in high wind with trucks driving past the person on the other end can't hear shiiiiiiiiiiiiiit it's spectacular. I will say that if you're going for Bluetooth headphones, make sure your phone supports at least BT 5.0 and AptX. That's going to give you the best experience. The Momentum 4 are $300ish USD and very worth it. If you're even a bit of an audiophile don't even look at the Sony's. Do look at the Bowers and Wilkins PX7S2 and the PX8 but those are starting to get into the big bucks. I also have the Focal Bathys which is the second most expensive bluetooth full size after the Mark Levinson 5909. Bathys is worth it but I only have them because I'm a curious single loser with no wife or children and I can buy stupid things that I don't need. If you can afford the Bathys they're delightful but you don't need to go that extreme coming from SR80s. I think the Momentum 4 might be ideal for you in terms of cost effectiveness and providing what sounds like an upgrade coming from your Grados.

Having said aaaaaaaaalll that, if you LIKE Grado (Grado sounds great I just hate the way they look. I've had SR80/125/225 myself) and you want good grado, Get SR325's and pick up a decent quality Dongle DAC. That's going to put you above the Momentum 4 price wise but will arguably give you better detail and a more natural sound, which might be good depending on what you listen to. Still open back though so hard to blast loud on public transit etc.

Oh sorry- totally spaced on these I keep forgetting they exist. Oppo PM3. $399 on Amazon.com (you have to click them then click see all buying options and there's only one seller).

I used to have these and had to tragically sell them when I ran into financial trouble BUT this is the one planar magnetic headphone that you can run off pretty much anything and it sounds good. You can even run them off those little 3.5mm to USB C dongles. That's not ideal, and I'd still suggest at least a dragonfly, but they sounds pretty damn good straight off a phone, and they will definitely get loud with no clipping. You get most of the planar benefits that would come with the 400SE/400i/4XX with less drawbacks (better build quality, closed back, smaller driver is quicker and doesn't get muddy, better bass). The only place I'd say the 400SE beat the PM3 is in smokey female vocals, which most music doesn't have, but if you were Dianna Krall's number one fan I'd stear you to Hifiman or LCD.

Sorry for 3 posts in a row. I'd say my 2 best recommendations that are the most bulletproof are Momentum 4 and PM3. PM3 is $100 more but sounds like $300 more, but is also not wireless, and you really ought to consider the Dongle DAC. Momentum 4 is $300 one time and done.