What alterations can be carried out to a network that has reached its
capacity in terms of nodal connection?

One word: Subnetting.

However, the devil is in the details.  What physical topology of
network?  What logical interface (Ethernet, Token Ring, FDDI, ATM,
etc) is the network?  What limit has it ran into?  A hard limit of the
cable or node count?  Or a protocol limit?

With a bit more information, a full answer could be developed.

There is not any specific physical topology, logical interface, limit
and the question just needs a brief description about the alterations
can be made to a network in general when that has reached its capacity
in terms of nodal connection?
Basically that was a question given in an exam for a second year Bsc
Computer Science student. So I think the question was not too specific

Thanks for the comment