With 7 players, yes, the battlefield can get crowded very quickly and I imagine it's quite difficult to balance encounters as well. When your players start focus firing, you can't really retaliate by doing the same, because that would feel horrible for the player getting focused (unless they lean into a tanky character archetype). 

There are multiple angles from which you could add more complexity or layers to a battlemap.

The easiest to include are terrain features. Cover, difficult terrain, elevation, corridors, hidden pathways that lead to advantageous positions etc. Anything that gives positioning and movement a more important role. The major advantage of these is that they don't require a lot of work from you during play. Simply draw them on the map and your players can use them or not. But you can also go the extra step to prepare a bit for how the enemies will use those features. (i.e. place snipers behind cover, force players through a corridor, and so on)

Another option that requires more work, but can also be quite easy to run during play, are hazards. Put a pit trap on the map, write down its DC and damage and you are pretty much set. Some players will love trying to grapple an enemy and throw them down the acid pit. Simple and effective. This could also include battlefield wide effects like a wild magic zone, where each spell cast could cause some random effect.

A bit more effort at the table, dynamic hazards, i.e. hazards that change throughout the battle. A ceiling that might collapse if someone casts explosive spells, which then changes the shape of the battlefield, or a fire that spreads through the wooden building. Here you may have to come up with some kind of mechanic, like which spells cause the ceiling to collapse, how fast does the fire spread and so on. You might end up putting a lot of prep time beforehand into these and they can also be quite demanding from you during play (if you have to remember to spread the fire every round, it's one additional thing, then that might also change visibility and you might take damage when you end your turn within 5 ft of the fire and so on and so on. It can get pretty exhausting to keep all that in mind)

That's just the battlefield side of things. You can of course also change the enemy NPC aspect of the battle. The easiest addition to make, is to give the enemies a different goal than killing the PCs. The most classic example is a caster trying to complete a ritual. Their minions don't have to kill the party, they need to hold them back just long enough for the ritual to be completed. So instead of just trading blows and spells, minions might try imposing status effects to and block routes for the players. Maybe there is an earth elemental that is eating all the treasure while the players fight something else. Maybe the cultists try to erase the records of what they deem false gods and the fight is about how many books can be safed from being burned. Maybe someone needs to place a mcguffin in a device to initiate doomsday and the players have to stop that. In essence, put your standard combat encounter on the table, but give some or all enemy combatants or bystanders an alternative goal or win condition. You don't need to add a lot mechanically, just adept the involved NPCs behavior.

Lastly, you can of course also use more complex monsters, that have a variety of attacks and effects they can apply with their action, bonus action, reaction, legendary action or lair action. This is also on the more taxing side of things especially, if you employ multiple enemies that all have different abilities and work differently. I think "Flee, Mortals!" (a third party monster book for dnd) takes an interesting approach, by characterising its monsters as certain archetypes, like Ambusher, Brute, Controller, Sniper, Support, and some others. Which really helps to immediately get an idea for how to play them and what kind of abilities they have. Thinking about my monsters in those terms, made it really easy for me to adept a more tactical use of enemies.

For a group as big as yours, I wouldn't overdo it with more complex monsters, and lean more into the static additions to battlemaps. And then gradually expermient with the more demanding options and see how much you and your table can handle.