What means "modified"?
Assuming that your dipole elements are long enough for the lowest frequency I got good results with my antenna designs when I made the longest dipole for a 7% lower frequency than required. For example: if the lowest required frequency is 80 MHz, I designed the longest dipole for 75 MHz. That resulted in a pretty good and flat VSWR at 80 MHz.
The next important issue is the coupling of the koax cable to the two booms, I got good results with a short piece of chopper formed in a double S, one end as wide as the boom itself, the other end as wide as the drilled-together cable. This avoids instant impedance changes. This is quite important and may spoil overall performance.
The third important thing is that the booms increase in distance to the lower frequency dipole elements. Look at the LPDAs from Schwarzbeck, their antennas are made in this way. This leads to a constant impedance. I started with the upper frequency limit, adjusted the boom distance for lowest VSWR, then I adjusted the lower end for minimum VSWR.
Another important issue is to balance the antenna with a ferrite bead of proper size (and in the case of transmission with proper power handling capability). Omitting this may result in distorted antenna pattern as there may be standing waves on the screen of of the cable.
With a proper design there is no requirement for external impedance matching, the LPDA can matched pretty good to 50 Ohm over the complete frequency span.
CU