What mechanisms could prevent monetisation of public debt from driving up asset prices?

All OECD countries are now monetising public debt. As the excess money is reinvested in other asset classes, one expects this sharp increase in the money supply to sharply drive up asset prices (equities, real estate). We want to examine this mechanism more closely in order to identify: What may lead to a sharp rise in asset prices (equities, real estate). It is the increase in wealth on the back of the increase in bond values, caused by the fall in interest rates, and the fall in the optimal weight of bonds in wealth, also caused by the fall in interest rates; But also what could keep asset prices from rising. This would happen if demand for transaction money rose due to the fall in interest rates and the resultant increase in production, provided it absorbed the increase in the money supply .