You can certainly do so: it's been done many times in the past, and can be done even with a written constitution. The most recent famous example that I know of would be how the Nazi party used the Enabling Act, 1933 and Reichstag Fire Decree, 1933 to amend the constitution by essentially neutering all the safeguards, and used force to ensure that they could stay in power. Julius Caesar's reforms follow in a similar vein.
For someone to successfully force change like this, you generally need a political system that is unstable and has no strong (or at least effective) checks and balances. Additionally, you need the support of the military because otherwise they will generally support the existing structure.
Other less extreme examples I can think of where a system has changed to another system would be former colonies adopting new constitutions (e.g. Ireland and Pakistan), or where there has been significant change in the country's model (e.g. South Africa). Again, you need support, but this time it is within the existing political and judicial framework.