Sorry for the long post, but to shortly answer your question: No, Beastmasters cannot.
This is a bit of an issue in the BST community right now, among other things and I'll detail it a bit (it is relevent to the topic).
Early on, BST get all sorts of options when it comes to pets and areas, but later on that changes (as with everything in this game) and options slim down. A lot of BST are a bit upset with the lack of powerful jug pets 65+ (this does pertain to the thread, so just hear me out) and the fact that no mobs in dynamis are charmable and therefore they are stuck with jugs.
After level 65 BST, all but like 3 jugs are obsolete. Jugs have a level cap, and as a result once you are over their cap they no longer keep up with you in strength, and become increasingly useless. A table for reference:
To use Name Summons Cap
23 Carrot Broth Hare Familiar 35
23 Herbal Broth Sheep Familiar 35
23 Fish Broth Crab Familiar 55
23 Fish Oil Broth Courrier Carrie 75
23 Alchemist Water Homunculus 75
28 Humus Flowerpot Bill 40
28 Meat Broth Tiger Familiar 40
33 Carrion Broth Lizard Familiar 45
33 Bug Broth Mayfly Familiar 45
33 Seedbed Soil Funguar Fammilar 65
38 Tree Sap Beetle Familiar 45
43 Famous Carrot Broth Keeneared Steffi 55
43 Singing Herbal Broth Lullabye Melodia 55
51 Rich Humus Flowerpot Ben 63
51 Warm Meat Broth Sabver Siravarde 63
53 Quadav Bug Broth Shellbuster Orob 65
53 Cold Carrion Broth Coldblood Como 65
63 Scarlet Sap Panzer Galahad 75
75 Sun Water Amigo Sabotender 75
As you can see, 65+ the only jug pets that remain an option are Fish Oil Broth, Alchemist Water, Scarlet Sap, and Sun water. The problem?
Courrier Carrie's Tp attacks sucks, thus making her a not so great jug to use in place like Dynamis.
Panzer Galahad is nice somewhat better, TP attacks are a bit more worthwhile but also more expensive than Carrie.
Forget about Homonuculous, making it is very expensive (something like 10-20k PER JUG) and finding it on AH is close to impossible (and again, very expensive).
Sun water, the uber expensive jug. It's a Cactuar type and can use 1,000 needles. It costs about 60k per jug, and as much as 400k per stack. On top of that it only lasts 15 minutes.