No, you cannot do this. Spellcasting foci are discrete items in the rules.
The fact that Chapter 5, Equipment has discrete entries for each type of spellcasting focus -- arcane, bardic, druidic, and holy symbol -- indicates that each focus is a discrete object. The equipment chapter lists the various mundane weapons, armors, and other pieces of a gear an adventurer might come across or want to buy throughout the course of his or her adventures.
The equipment section has several sections. The one we are concerned with is the one titled Adventuring Gear.
The introduction for this section says:
This section describes items that have special rules or require further explanation.
As we read through this section, we see many different items listed, from alchemist's fire to ball bearings to potions of healing to 10' telescoping poles. We also see that for each type of spellcasting focus, there is a discrete entry.
Using the rules and information in the book as a basis, when a character in game goes to the store and buys a bag of ball bearings, he doesn't get to ask the shopkeep if his bag can be special and also include caltrops. Even though ball bearings and caltrops serve a similar purpose and are used in a similar way, you can't combine the two into a special bag of ball-bearing caltrops. They are discrete items described separately in the book.
Now, at this point you might say, "well, what's to stop me from mixing those two items together?"
The answer is, simply, nothing. The rules don't say anything at all about that, so if you want to it's up to you and your DM to determine how that works. Still, it's not something the rules say you can do with those items.
We can apply the same logic to spellcasting foci. Each focus type has its own discrete entry in the book. There is an entry for arcane focus, for bardic focus, druidic focus, and holy symbol. Each object is a specific type of adventuring gear that, according to this section of the book, [has] special rules or require[s] further explanation.
Furthermore, when we look at the table of adventuring gear, we see specific items (5e SRD or Basic Rules):
Arcane focus
Item |
Cost |
Weight |
Crystal |
10 gp |
1 lb. |
Orb |
20 gp |
3 lb. |
Rod |
10 gp |
2 lb. |
Staff |
5 gp |
4 lb. |
Wand |
10 gp |
1 lb. |
Druidic focus
Item |
Cost |
Weight |
Sprig of mistletoe |
1 gp |
— |
Totem |
1 gp |
— |
Wooden staff |
5 gp |
4 lb. |
Yew wand |
10 gp |
1 lb. |
Holy symbol
Item |
Cost |
Weight |
Amulet |
5 gp |
1 lb. |
Emblem |
5 gp |
— |
Reliquary |
5 gp |
2 lb. |
Musical instrument
Item |
Cost |
Weight |
Bagpipes |
30 gp |
6 lb. |
Drum |
6 gp |
3 lb. |
Dulcimer |
25 gp |
10 lb. |
Flute |
2 gp |
1 lb. |
Lute |
35 gp |
2 lb. |
Lyre |
30 gp |
2 lb. |
Horn |
3 gp |
2 lb. |
Panflute |
12 gp |
2 lb. |
Shawm |
2 gp |
1 lb. |
Viol |
30 gp |
1 lb. |
Notice that in the above list, the emblem does not list a weight. In accordance with the description of the holy symbol entry in this chapter, it could be an emblem on a shield, so in that case it has no weight of its own.
If the entries were not discrete -- if there was one entry that said "Spellcasting focus" and it had rules for each spellcasting type -- and there were not specific foci that you can actually purchase, with costs, then I can see a case for combining multiple foci into a single item. As it stands, the rules are clear -- one entry for arcane focus, one entry for druidic focus, one entry for bardic focus, and one entry for divine focus. They are discrete items by the rules and combining them into some other object not outlined in the rules is entering house rule territory.