well you can do that but you might as well do a three way ligation directly into the vector. It is the same as a standard ligation just add the fragments as 1:1:1 molar ratio and it will be fine. However, if you have blunt ends or single base overhangs you will need to adjust the ligation mixture.
Unless you have some way of purifying the "correct" ligation product, prior ligation of the two fragments won't solve much and may waste your time (the desired two-fragment product will not be the only product: there will also be recircularized monomers, recircularized dimers, etc). The best course of action is to follow Hanna Alalam 's advice, but take into account that the odds of obtaining the correct assembly will be lower than usual with the three-way ligation, so you might want to screen a bit more colonies than usual. Also, if redesigning the primers is a possibility and you do not succeed in your first try, PCR-SOE as suggested by Reza Hadavi is a safer alternative.
i did that before, 1- ligate the first gene in the plasmid then ligate the second genes in the plasmid with the first gene, take care that you should use enzymes that don't cut in the new construct. there is also a better way but really more expensive, is to synthesize the whole 2 genes together commercially (like genescript or whatso ever, then insert them as one gene in your plasmid. you have also a third choice which is a kit by Englnad biolabs which will ligate all the entities together but I really cannot remember its name.
I'm also dealing with a Problem and I would like to ask about your opinion...
My Vector Backbone (same Plasmid; but cut from different regions for different genes) is varying 3.3kb to 3.4 kb and my inserts sequences are 2.1kb, 2.3kb and 2.3kb.
I tried with;
-1:2, 1:3 ratios,
-used fresh Buffers,
-didnt expose DNA sequences to UV too Long while cutting from gel,
-after isolating DNA sequences from gels, i run them to validate sequences and they were correct too,
-DNA concentrations (Vector Backbone) were changing between 9.5 to 11.5 ng/µl (and I increased Vector DNA amount with insert DNA amount regarding to 1:2 and 1:3 ratios too..)
-At the end of the Ligation, samples were incubated at 16C for overnight +/-18-20hrs
-agar plates were prepared fresh,
I would like to hear your recommendations & ideas..
I purified my digested fragments from gel(two insert and a vector: every insert had one ligation sticky end to the vector in proper direction and one sticky end to attach together), then I measured the concentration with nano drop. Finally I add them together(all of them) in a tube with 1:3 ratio for ligation of each fragment in 10 micro liter total volume.
( normally a vector to insert ratio of 1 to 3 is used of cohesive end ligations )
I also used this webpage for ligation calculation.