I can think of two different ways of approaching this question, depending on what you mean by "conventional technologies". As I think both would be interesting questions, I will attempt to answer them both.
No more conventional technologies to discover
Our own history has involved moving on from one technology to the next as we discovered better ways of doing things. I would call that a series of conventional technologies, even though each one is novel when it first appears. If you are asking what would happen when there are no longer technologies left to discover (due to a species reaching the current limit of its ingenuity) then the next technological step could not be a discovery. In that case the next technological step would be some kind of compromise. Unable to use technology to continue feeding an ever growing population, compromises may include population restriction, rationing of resources including food and water, or even reduction in body size to allow a larger population of smaller creatures. Metabolic rate may also be artificially restricted so that a slow living population can support greater numbers than the available energy would otherwise allow. When technology can no longer be used to provide more, it may be used to restrict numbers, restrict access to resources, or restrict the size or life rate of individuals.
Given enough time these are all natural effects on a population in a restricted environment. For example, dwarf dinosaurs and reduced metabolic rate on islands. Technology may be used to speed up these effects in order to avoid conflict and suffering. It may be used to enforce equality in suffering so that everyone is a little bit hungry, rather than some starving. In the extreme case, a species may become unrecognisable due to the changes made, possibly even ceasing to be organic eventually.
The next conventional technology
If instead you are looking for the next conventional technology, to allow continued growth of a population that can no longer be sustained by its current technology, then there are two ways of searching. You can look back or you can look forward. You can look back to earlier times and see if a technology that has been abandoned for being less practical might be adopted again due to being more efficient. Sometimes new technology is not more efficient that the previous one, just more convenient in times of plentiful resources. Looking forward is more difficult unless your world has technology similar to our past, allowing you to use our present as an estimate of their future. If you want to predict technology that we don't yet have ourselves, this is more difficult but there are some things you can do without needing to make genuinely new inventions.
Look at the theoretical limits of current technologies
For example the limits on communication, transport or computing. It is unlikely you can predict the specific details of improvements in computers over the next century, but you can read up on the theoretical limits of computing. This way you can give your world a level of computing power which is theoretically consistent with the amount of available energy and materials they have, even if you don't explain exactly how it works.
Necessity is the mother of invention
A good prompt for your imagination is to ask what a population in such a situation would most need. This won't give you the inner workings of the resulting technology, but it will allow you to present a more believable combination of unexplained (or partially explained) technologies.
Be specific about what is in shortage
It's not easy to imagine new technologies as a result of a shortage of everything. It's a lot easier to come up with new ideas if you just think about one specific shortage. For example, in a world with a water shortage you can think about what problems that would cause and what alternatives could be used. You need to drink water, but you don't need to flush the toilet with it. You can separate the current uses of water into essentials and luxuries, and come up with alternative technologies for the luxury uses and more efficient approaches to the essential uses. By imagining one shortage at a time, and adding to them, you can build up an idea of what might happen if a population was subjected to a number of different shortages over time.
There are of course far more specific potential answers, which you can access by posting further questions and narrowing down your requirements each time.