Can the basement membrane of blood capillaries expand?
It's a good question.
Though there is hardly some evidence to answer your question.
However I will share what all I found.
So in capillary basement membrane, mostly collagen type 1 and 4 are  present.
Now collagen type 4 aids in elongation of the new capillaries-

in the ex vivo rat aortic model of angiogenesis using a type I collagen matrix, type IV collagen promoted new vessel elongation and survival in a dose-dependent manner compared with controls (no type IV collagen), which grew until day 9 and then regressed during the second and third week of culture (treatment with 3, 30, 300 g/ml of type IV collagen in 43, 57, 119% increase in microvascular length) [139]. In all then, type IV collagen seems important for stability of blood vessel formation.

The collagen in capillary basement membrane impart mechanical stability to the vessel.
Also elastin is a component of the basement membrane. Reference
Now though I couldn't find that it's the elastin of basement membrane only, but-

Comprising 50% of the dry weight of major arteries, elastin is the most prominent ECM protein in arteries [43]. In vessels, elastic lamina alternate with rings of smooth muscle forming a strong, flexible part of the arterial wall [43, 44].

Here is the article